Note: Sorry for the wall of text. Didn't think it would take a post this long to type that out
As a personal taste, I really dislike crossovers for a lot of the reasons already given. A lot of the time, people rely too heavily on the appeal of taking two very popular and well known fandoms, mashing them together, making a few offhand references and in-jokes for each fandom, and calling it a day. The truth is, a lot of the time it works. Doesn't always make a good story, but if the fandom you're crossing over with is popular, it'll often be enough to get your story some fans regardless of the actual content of your story. I usually look at a crossover story and think, "Alright, that's all well and good, but X reference had no actual content," or, "Why was X fandom even brought in when it didn't add anything to the story?"
That said, I'm going to play devil's advocate in this thread partly because, while I generally dislike crossovers, there are some points in their favor worth making, and partly because I see a lot of usernames in this thread that I read posts from in the FF forum and nine times out of ten say, "Yeah, I agree with what he/she said. I like the cut of that poster's jib," and want to see what y'all have to say about a worthwhile topic.
I think of the "mistakes" of crossover fanfiction not as mistakes, but "hurdles". If you're writing a crossover, you've got a lot running against you if you want to write a story that sells itself on its own merit (we'll get back to that point later, but that seems to be what's up for discussion in this topic, so I'll hit that first). The one brought up most is the issue of "mismatching"--how can you fit the two together when the content of each fandom is at odds with its partner?
Hammering a square peg into a round hole is about the best way to describe it, but I don't think it's impossible for two fandoms to be welded together simply because of those differences. It might not be everybody's taste, but you can still make a story that stands on its own merits out of it. It all depends on how much effort you're willing to put into justification. For example, Hanako delivering her balls-out-middle-fingers-up spinning roundhouse in the world martial art tournament. That's not the Hanako we know, but has it destroyed her character? Not necessarily, but you've got an assload of explaining to do. If she's going to be fighting with the Tekken and Co. people, she needs to know how to fight. It's not established in Katawa Kanon that she does, and evidence would seem to suggest otherwise. But there's also no evidence that concretely rules it out.
The general rule to justifications is that the more outlandish the event you're trying to sell, the earlier in the story and the harder you have to hit on the point. Hanako probably did a lot of physical therapy. Who is to say martial arts training couldn't have been a part of that. But, if the first time the readers hear that Hanako has a 4th degree black belt and has been training since her injury is when she throws the kick, they're going to close their browsers in disgust. Since it's a pretty major change from what readers are going to expect from her character, it needs to be addressed early, and it needs a good deal of focus before anybody is going to believe Hanako is a tournament fighter. It can't become her whole character--she still needs to be Hanako--but it can work, at least in the context of the story you're writing.
Giving Hanako the ability
to throw the kick doesn't justify the whole scene enough that people are going to believe it, but we can tie hurdle number two--the originality issue--in to actually help
us here instead of hurt the story. And no, before you smack me, I don't mean that it's original and has merit on its own just because it's the only story where Hanako throws 720 jump spin hook-kicks. If you're able to justify her ability to throw the kick, you still have to justify her reason to throw it. Hanako is a little timid. Kind of shy. Probably not the type of person to fight in a tournament like that. You can tie in her reason for throwing the kick along with the originality, as well as justifying the story as a crossover instead of just using OCs. Ultimately, something needs to kick her (no pun intended) out of her shy self and make her a fighter. Maybe it was in her all along, but she just needed a push. Maybe even she didn't need a push, but wanted to hide it because she knew that if she lashed out, she'd get more stares, and she'd be seen as more of a freak than she already imagines people see her as. However it's done, make it a main theme, if not THE major theme of the story.
Unfortunately, I'm not familiar with any of those fighting games you listed (except for Battle Raper, that game was the sh... wait, what?
Forget you heard that). I am familiar with a similar "tournament style" game--Twisted Metal--so I'll use that for this hypothetical simply because I'm familiar with it (Yeah, this brings up the familiarity issue of "Mistake Number 3", but we'll get to that). In Twisted Metal, contestants fight in tournament style battles for the grand prize of having any one wish they desire granted (with often unintended results). Let's use that as the basis for the tournament, since this is a mega-crossover with a whole bunch of different "tournament style fighting" fandoms. I also like the Twisted Metal format because the prize is always directly related to what makes a character him or herself--their ultimate desires. This gives you an excuse to examine the core of what makes Hanako herself.
If you're doing a crossover that stands on its own merit, you need to bring something to the table that any of those fandoms don't have on their own. In this instance, we're taking characters from Katawa, and a slew of fighting games, and putting them in a fighting tournament where the prize is any one wish granted, as per Twisted Metal. So what wish from Hanako could be powerful enough for her to step out of her meek shell and put on the gloves? That's free game, and as long as you can make that wish strong enough, you can justify her fighting. Maybe her wish is that the fire she lost her parents in--and that took half of her body--never happened. That's a full reset button on the event that, in her mind, ruined her life and has driven everything she's become since. I could buy it, with a little sales talk. But wait, plot twist! She falls in love with Hisao, who can't
fight for himself because of his heart condition. She's conflicted--does she go ahead and continue fighting for her own wish, or does she use her wish to cure his condition instead? There's a lot to explore there, and that's looking only at the Twisted Metal element that was introduced.
So what about the other contestants? Why bring them in from other games when the story above can be told only with the Twisted Metal cross and a few OCs for her to kick around? If another story is crossed into a crossover, it has to bring something along with it to the table. And it easily could. Those other characters have desires themselves. What are they fighting for? How does Hanako feel about their reasons for fighting. Better yet, develop another fighter from one of those other games, and make them a major character, too. Pick somebody who has a goal that's very similar to Hanako's. Are his/her reasons for pursuing that goal the same as Hanako's, or are they different? Compare/contrast. How does Hanako feel, knowing that this character is essentially the same as she is, and she has to crush everything he/she is fighting for? Even better, maybe there's also a character that has a wish that's at its base is the same as hers, but in some way perverted, or the person is a monster, or the wish--while pure in heart, and possibly selfless--is something that she believes is ultimately wrong. You can develop characters from both/many fandoms, show how their interactions with people outside of their home base reveal their views in ways the people from their own fandoms couldn't, and even in some way change that person. They can change Hanako, too. Make the square pegs the themes you fit in your round hole.
Hurdle Number Three is a little different from one and two in that it's harder to address at the same time (not impossible), while one and two can (and probably should) be jumped in conjunction with one another. The first question you have to ask is what audience you are writing to. Are you alright with writing specifically for audiences that know the fandoms involved, and alienating those who don't? Yes? Alright then. You're good to go. So you'll lose people outside of the loop on the way. If you know you are writing for a particular audience, and you don't care about grabbing people outside of that audience, then there is no harm in saying, "Screw it, you're on board or you're not, let's rock-and-roll!" People who know the fandoms will follow the story. People who don't won't, but they were never supposed to anyway. Fanfiction success.
If you want a wider audience, though, you will need to do some explaining. This is where Silentcook's problem of explanation comes in--your audience already knows at least half of the material, and you will lose everybody if most of your story is explaining the other half to each side. This is something you can minimize the effects of, but can't completely eliminate--one of the real problems of crossover writing. One solution could be to explain everything only
as one character sees it. Back to the hypothetical, we'll use Hanako. Since this is a Katawa forum, we can assume that everybody is familiar with Katawa Shoujo, so we'll immediately empathize with her and understand the KS elements of the story. That leaves the elements of the other fandoms that are crossed into KS. Don't try to explain things objectively. That's where you'll lose people. Explain them as Hanako sees them. This is also how you can roll Mistake Number Three into One and Two. Hanako needs a reason to fight. Through that, you necessarily explain the Twisted Metal element as far as any reader of your story reasonably needs to know. Then explain the other elements as Hanako encounters them. Meets a fighter from Tekken? She doesn't need to know his backstory--and probably shouldn't, if there's no reason why she would have met him before. You can keep the other fighter's personality, style, desires, and quirks intact, but reveal them to the audience as Hanako encounters them. That way, you're not info-dumping to the reader. Instead, you're having the reader digest the information along with Hanako, and allowing the reader to see how Hanako interprets it. You can tie all of that directly back to your themes, and then you have originality to boot.
There are the three hurdles mentioned if you're trying to write a story that stands on its own merit. I do have a few separate points in defense of crossovers though.
First, this is all assuming that the story has to stand on its own merit. This is largely going to depend on your view of what fanfiction should be, but I don't see anything wrong with a fanfiction
story that doesn't stand on its own. Ultimately, fanfiction is something written for fun. A lot of people DO try to learn to be a better writer through it, but if your goal is to be a better writer, you should really be writing original fiction anyway, not fanfiction. That's not to say you shouldn't ALSO write fanfiction, or that you can't learn through it, but there is less you can really work on with fanfiction than there is original fiction, and if your goal is to learn to write, fanfiction is what you should write for fun on the side to strengthen things like writing style (grammar, sentence structure, word choice; the technical aspects of writing) and story consistency (keeping things coherent throughout a single, continuous work of fiction). The truth is, though, that most fanfiction is written simply for fun, and a lot of readers are reading for just that. What's the harm in providing a product that's in demand? It might not be a workable story on its own merits, but if you make a certain audience happy with it, you've achieved every goal you set out for. That would never stand for a work of original fiction, which by its nature requires a heightened standard of review. I'd argue it can
stand for fanfiction.
All of that "you should be writing original fiction instead" stuff aside, there really are
some things you can work on with fanfiction that you can't with original, and even more specifically, there are things you can work on with crossovers that you can't with straight fanfiction. Justification of the type described is one. It can be an awesome writing exercise to take two fandoms that people say could "never fit together and work", and then make it work. It'll be difficult, but if you can come up with strong enough justifications, it's possible. There is nothing so outlandish that it can't be done. It all depends on how much work you're willing to put in to justify it.
Ultimately, though, I don't think the problem with terrible crossovers is a problem with crossovers themselves. Are they hard to do well? Yes. But (TL;DR): If a person isn't willing to put the effort into writing a "good" crossover, they probably aren't willing to put the effort into writing a "good" story period.