It should be as simple as a check list in the options menu. I know a lot of people play with the sound off, and while I like to play music in the background I still enjoy most of the dialogue and banter in game. However, there are some heroes I just can't stand listening to, Iceman being the worst. Love the voice actor, but he has the absolute worst dialogue in any modern game I've played. His voice alone deters me from playing him sometimes.
Perhaps they could even add a slider or something similar to the old BG and IWD games where the characters talked a lot, sometimes, seldom or never.
Maybe this is a stupid idea, but I just prestiged Iceman to red and wanted to shove cucumbers in my ears...