There are characters built around a game and games built around a character.
Say for Gears of war, I have no emotional ties with the characters, so it wouldn't matter to me if Fenix was a frog or a zombie with an anger issue, as long as he/she/it is doing what they do best, tearing locusts apart with chainsaw guns. The same could be said about the likes of Halo Tekken, Tomb Raider games and other similar titles. I think the industry has demonstrated how much we still care for Lara Croft, considering we have Uncharted and Prince of Persia now.
Cod Games are the same, replace tom with bishop and kate with faye and it makes no difference to me, I am here to shoot iraqis / russians, when do I start.
Then you have those games that are based upon character development, take Final Fantasy 7 for example, Sephiroth (while he is a plamnk) IS the villain, replacing him with a clown would not have the same dramatic effect of evilness, as with Joker is to batman, replacing Joker with masterchief would definitely be noticed. Other such games include Duke Nukem (before he dissappeared for years) as a Duke Nukem game was....well a Duke Nukem game, it was classed as an FPS, be we know it as a Duke Nukem game, simply because Duke is so bad ass and memorable. I can't think of many other FPS characters like him if any at all.
This is why character development is important, but the problem here is that when a character is focused on more than the gameplay, when the characters story comes to an end, so too does the gameplay. Take God of War for example, Kratos IS the God of War, and he's so kick ass that he's killed all living things. Even if you could, how would you create a spin off of that, the conclusin is that everything dies because of Kratos. The only way you could continue that game of chess is if you chose a different mythology and created a different angry character to go with it....and we all know how well Dantes Inferno performed ¬_¬
So yeah, that theory is flawed.