I think the reason that I don't regard the characters of FFVI as highly specialized is that I started with FFIV. The stat differences among characters are far more stark there than in FFVI and there isn't much flexibility to change them (other than choosing your equipment there's basically nothing). Only certain characters can learn magic and the spells they can learn vary. Granted some special abilities may not be terribly useful but they each have their own abilities and not much in the way of customization crutches to get around that.

Therefore, I tend to regard VI as the start of the trend continued in later games toward more customization over set individuality. I do agree though that characters with individuality are better. I tend to think some later entries like FFIX and FFX maintain that better than FFVI though. It's true that in FFX characters can lose all of their individuality, unlike FFVI, but the way the Sphere Grid is setup you can't really get most people out of their set classes until late game, it pretty much lays out for you the path to keep them on the one class track with maybe some dual classing late game. Beyond that you'd really have to grind to take away all individuality. A lot more than just to teach everyone the best spells in FFVI.