(My first reaction was to say " well, that is a bit of a self-proving argument" or something to that effect, but I suppose we are basically forced to work backwards when talking about this since none of us are game developers.)
As such I will say that while Potemkin is a (more than) decent example of a character who can succeed despite not having an air-dash or much mobility in general due to the other tools–fucking Slidehead and its accursed unblockable shockwave–that the character is given as compensation, that is not quite what I was trying to get at. I was more asking if non-universal air-dashing seems like a good thing from a basic design standpoint given that the characters without the air-dashes stand a significant chance of being screwed over and will doubtless always need some type of compensation for lacking a universal tool. Still, that is my fault for not quite clarifying things as much as I should have.
I will use (Ultimate) Marvel vs. Capcom 3 as an example of, once again, what I think should not be done. In that game, as everyone in here probably already knows, not every character has the benefit of having an air-dash unfortunately. For example, all of the Resident Evil characters lack an air-dash, though Wesker effectively has one given his teleport, which is part of the reason that he’s the best Resident Evil character in that game, though I am getting ahead of myself a bit.
Given who my main character was when I still cared about that game, I will use Chris Redfield as an example of how not having an air dash or, really, any air options in general is highly detrimental. In general, despite being a space control zoner character in design, even if he is not having to deal with one of the slew of teleporters in the game, if Chris ever super-jumps, then due to his lack of air-dash, he is basically always doomed to land on an ambiguous mix-up of something if he doesn’t call an assist before doing so or have a land mine already out to prevent someone from just ground dashing in on him. The fact that he lacks any valid air-to-air options if someone is not either right next to him or diagonally under him is easily his biggest flaw as a character. I can tell you that if this were any other game, then match-ups like Chris vs. Trish would be basically 0-10. As it is, it is a bit of a secular miracle that Chris is only as low as mid-tier, though that is arguably mostly due to just how incredibly good his land-mines and magnum special moves actually are even when compared to the general bullshit in that game.
More generally, if you look at all the characters in the game, you will notice that pretty much all of the lower end characters have either non-existent air mobility or at best have a terrible version of it. Hsien-ko is a prime example of the latter, having what’s easily the worst air-dash in the game to the point it is usually better not to use it, especially since it unnecessarily got hit by the overall air-dash nerf going into Ultimate, which is just another example of how rushed the game is, but I digress. Hsien-ko is a rather tragic example, really, given that her utterly crippled mobility is basically the only real thing holding her back from being an at least decent character since she has excellent normals and at least the one of the best hypers in the game.
On the other end, pretty much all of the top tier characters have air mobility and tend to have it in excess. I will grant that having excessive air mobility does not automatically make someone top tier, as evidenced by how Trish somehow never manages to make it into Top 10 characters on anyone’s list (that I am current aware of) despite still being a great character, but it sure as hell does not hurt in the least bit.
Of course, this is all specific to one game, but it is perhaps at least indicative of what said change did to the series it is the latest installment of given I think pretty much every Vs. game before it had universal air-dash as a mechanic; I am admittedly unsure about Tatsunoko vs. Capcom, however, given I have never played that.
All things considered, at the very least, UMvC3 made me decide that basically universal air-dashing either has to be in a game where everyone can super-jump and super-jump height is thus a regular part of the game or you have give the characters without air-dashes some type of compensation, likely aerial, to make up for lacking it. It still bugs the hell of me, for instance, that neither of Jill’s Level 1 supers/hypers can be used in the air for some inane reason, to say nothing of the whole DLC idiocy and them nerfing her before anyone even discovered her Mad Beast unblockables, but, again, I digress.