Well for me it is exactly opposite. It _immensely_ breaks my immersion if my character does _NOT_ speak his/her lines. I actually fail to even understand how it can break immersion for someone if he/she does but if yes - I agree they could simply give you an option to turn it off. Lucky for you, that's a lot easier solution, than what I need to be happy.
Despite it's simplicity, what I want will probably not be in game and we will need modders to get it done.