When I talk about "character advancement" with respect to RPGs, it's the game-y leveling mechanism I object to, not the idea of character growth per se.
If a character (as portrayed by a real person) "grows" through what they do as part of a story, great. If they gain more power by acquiring more powerful tools, OK (although that has some pathologies as well). But "growth" during the course of gameplay through some artificial system of character or skill levels, IMO, winds up distorting actual roleplaying. How is grinding for XP anything even remotely like roleplaying?
Yes, of course the determined roleplayer can do so even in a game with character/skill levels. They just make it harder to do so compared to a game where everyone starts playing with a fully-skilled character. Wouldn't it be nice to have at least one high-quality game where playing a role wasn't tied to the leveling mechanism?
I believe that by advocating the design of a MMORPG without character/skill levels that are increased during gameplay -- a MMORPG that lets you start playing the full game the moment you exit character creation -- I'm actually promoting a game design that does a lot more for real roleplaying than the very Gamist designs that are pretty much all that are available currently.