Its worth mentioning that very few hollywood movies feature "normal" people in them, regardless of their race. Tom Cruise's character in the Last Samurai certainly isn't normal. Niether are most characters in action, sci-fi, suspense, comedy, horror, romance or most other genres. I suppose you mean you want more asians to star in human drama's and that sort of thing? It is worth asking if by "asians" you mean Asian-Americans or people actually living in Asia?
I think its mostly a question of marketability. A movie about normal Japanese people living in Japan would appeal to very few Americans because very few could relate to it. A film about normal Asian people living in the west (like the Indian family in 'Bend it like Beckham') would probably be a lot more popular, and I agree that it would be nice to see more movies like that made.
Still, this issue really has absolutely nothing to do with the Last Samurai whatsoever.