I personally think adding voices for our characters wouldn't ruin the immersion at all. (At least, for me.) Since we're the ones picking out their voices when we initially create them. For me it would only heighten the immersion because I'd be able to witness my character actually interact with NPC's and actually have an opinion. I think the only time I got to hear my character "say" something was when I first met Gaius van Baelsar, and even then all she said was "No..." but it still gave me goosebumps.

Perhaps as a sort of compromise, we as the player could select a response from a list. That way, we still have control over our character's choices. Sort of like how the voice acting worked in the walking dead game, which turned out very successful. Or, as another compromise our character wouldn't ever have to speak a full sentence but still vocalize phrases that would seem appropriate for any character.