The music thing has crossed my mind before, but I always run the game in windowed mode (I think that's the default). So it's really easy just to have a media player of some kind running in the background, playing whatever music you want. For Jak to implement music in the game, it'd either be an in-game interface/player that you can dump music files into, or Jak would have to start composing and producing his own music (or buy the rights to them).
I think such a feature would be cool, but I'd honestly rather the time and effort/expense be put into other positio- er, features
(though honestly, I tend to not play music, as it makes it harder to hear the heavy breathing and it adds to the realism. If the voices were louder and more porny, I think I'd be more inclined to play suitably porny music in the background)
I totally agree on having a variety of voices, though. Nothing is really said atm with the voices, but having some kind of tonal variety would add some personality depth I think.