This is ridiculous. I'm thinking of games with classes and free skills and the differences inbetween, and apart from combat, I can't think of anything significant from most (99/100) games. Combat has always been the dominating factor and THE motivator in RPGs and the differences between classes and skill have seldom meant anything other than melee/magic/ranged. If anything, there have been more skill based games where your choice of skills were more restrictive in a meaningful way than class based games where restrictions of classes were meaningless due to high combat frequency.
In the end, it's all about shit design vs. good design. Suggesting inherent superiority for either over the other is pretty stupid.
A Vampire implies an extremely specific gameplay mechanic and so the supporting skills/perks must also be extremely specific.
Where exactly is this implied, and in what form? I've yet to see anything remotely similar in any rpg type, and almost anything remotely similar in any other form of media. There have really been very few IPs where being a vampire meant a very specific and very restrictive transformation, like vampire characters being reduced to mindless killers, zombies, all with the same set of generic abilities within the IP.
From a gamist point of view, the notion of a vampire being a class in itself might be interesting in certain settings, but from a generalist and logical view, it doesn't make any sense with the vampirism in popular (and unpopular) culture so far.
Ummmm.... what? The fact is, a skill-based system implies that the skills are relatively generic unless you're dealing with something like VtM where ALL characters are vampires to start with.
Again, where why and how is that implied at all? Most skill-based systems have been terribly generic that tends heavily towards getting good at everything eventually, so whether you add vampirism into the equation or not, is utterly irrelevant.
Also, saying that ALL characters are vampires to begin with in VtM couldn't be any further from truth. Even if you're specifically talking about VtM:B, it has various straight human NPCs as well, where your choice of skills between fight/sneak/talk matters, despite the fact that Troika did a terribly shallow and stereotypical job handling the VtM PnP setting with Bloodlines, but did a pretty good RPG despite that shortcoming that has nothing at all going for it to support your argument.
I really don't understand where you are coming from with this "universally implicated notion: vampire=one single class" thing, and I definitely don't understand your problem with how skills play into it. According to your suggestion, we couldn't have any diversity with vampires, and have nothing like the cool vampire stereotypes in popular culture, like Dracula whose strength derives from his coercive charisma and elusive abilities, or D, who doesn't have much going for his character and social interaction but is a cunning fighter or what have you and his opponent in one of the animes, who's that IP's version of Dracula. Basically, what you're saying is as good as vampire=zombie because of the single type restrictions you propose.