I agree that some games should go down this route, but not the majority at the moment. The majority of games should be exactly that, a game, something quick and fun in my opinion.
When games become more realistic, in terms of graphics etc then maybe we can look at creating more character driven, emotional games. But at the moment, its kinda hard to become attached to a character when you see his hand made up of a block with fingers painted on it, or when you see a glitch in the shadows which causes a triangle of shadow to appear on his neck.
In other words, when games become more cinematic, then I think developers can start really thinking about adding cinemaesque style story telling and character driven plotlines.
Until then, its best to stick to stick to plain old fun!
PS: A good example of how improved graphics, direction etc can add to a games emotional impact is “The Chronicles of Riddick” where great graphics(if a bit glitchy), direction and voice acting can really add to the atmosphere giving it a more cinematic feel.
Its a pointer to where things are going with regards to technology giving developers better scope to create more cinematic style games.