I don't think many of these problems are really with the Nobodies themselves, but with KH2's writing and their execution therein.
My and almost everyone else's biggest problem with the way the Organization was handled was their lack of presence. But this has nothing to do with the Nobodies as a concept, and everything to do with the game's other, more glaring, narrative failings. I didn't really have a problem with the way the lessers were handled either, and (directed at Hakan Xatos' criticism) I don't think there was anything particularly convoluted about them. In the Secret Ansem Reports, and in the player's formal introduction to them by Yen Sid, it's made pretty clear that Nobodies are exceptional—as Seph just stated, not as many Nobodies are created as Heartless—and they're intelligent; not mindless attackers like the Heartless or Unversed. And in KH2, they would've only distracted Sora from the Heartless, which would've been counter-productive to the Organization's plot. For the lesser Nobodies to have played a bigger part in KH2 might've been nice, but it would've been just another example of the narrative contradicting itself. The story would've needed to take a very different shape in order to properly utilize them. As it stands, we're given a canonical (and fairly reasonable, imo) excuse for their low-key appearance. That being said, I agree that it would've been just as well for the lessers not to have made any appearance in the first place (not that I wasn't happy for what little variety they offered anyway). And the whole non-existence thing is silly, yeah. It could be argued, I guess, that their legitimacy is only in question because of their missing hearts, which, in KH, seems to be the primary self, but that's neither here nor there. In the traditional sense, they definitely exist.
On the note of their heartlessness (let me just take a moment to say that I agree w/ chu on this front; all Heartless have is hearts, and Nobodies DO have bodies (in addition to a soul), so, um?? These names might work figuratively if the literal didn't totally eclipse their meaning lol), I didn't find their supposed lack of emotion nearly so hard to believe as some of the posters here. You have to remember that all this really means is that they function basically like intelligent socio/psychopaths (I think krexia wrote an Axel-centric editorial for the site, ages ago, that touched on this a bit?), who know how to disguise their differences in order to manipulate [others, circumstances, etc.] to their own ends. Not to say that all of their behavior is necessarily appropriated, especially in the case of Nobodies who, obviously, were at one point capable of empathy and a genuine range of emotion. I think some of that is probably habit. But things like personality or charisma, after all, are not emotional expressions, but psychological. Like, someone mentioned Demyx earlier as an argument against this, but I think he's actually a pretty excellent example: All of his apparent personality quirks and "emotional" responses are utilized specifically to make himself seem harmless, to self-preserve, but he turns on a dime when finally forced to confront Sora in the Underworld, in a way that reads pretty uncannily to the player—illustrating that, indeed, he's been playacting all along.
On the other hand, I think Axel already makes it abundantly clear in KH2 that their heartlessness is ephemeral at best. I don't think the revelation in 3D was as much backpedaling as it was confirmation. And this is where, imo, things actually get convoluted. I think the Nobodies as a whole made more sense when we were led to believe they were only appropriating emotion. As they stand now, with their lil fledgling babyhearts, the entire point of their being is basically defeated. Like why even? I think most of us can agree that the series as a whole took a turn for the worse with KH2, but 3D in particular didn't exactly improve the situation, story or lore-wise.