I think his accent is cool
What's with all the spoilt upper movie goers these days. They've been so brainwashed by todays media that they believe his accent to be repulsive.
I think it's cool and it give his character a personality and charm unlike some actor out of New York, California or Britain.
He doesn't want to change his accent and that's his choice, and that's pretty ballsy. He knows it'll limit his career but he's proud of it, and that's a better person than someone who wants to pretentiously live and die the theater and get buried next to Malon Brando, whilst Billy Crystal is singing at his funeral.
He has a cool job and will just take what he can get out of it without losing self respect.