I agree with most of the points here about why muted PC = good. In addition to the various permutations of race and gender, not to mention origin stories (if a Dwarven Noble spoke exactly the same in all situations as a Dwarven Commoner, that would be kind of weird, no?), two other big reasons I like it:
1. We naturally associate voices with faces. Arguably, some voices 'match' certain faces better (e.g., it's off-putting to see a heavily built guy with a high, dainty voice). Even without this aspect, once a voice-face pairing has been made, it's very disconcerting to break that connection. I ended up deciding to stop customising my appearance in Mass Effect, because it seemed weird for the 'real' Shepard's voice to be attached to my customised character. This would be a bigger issue still in Dragon Age, I think, where repeat playthroughs are even more highly encouraged and customising your hero is a big part of the game rather than just making facial tweaks to the defined character role of Shepard.
2. In Mass Effect, the short phrases you selected were almost never what Shepard would actually say, verbatim; they would suggest the general content and attitude, but not exactly what was said. This just seemed like a space-saving idea or an odd design touch in ME, when the 'real' quote would then be read aloud. In Dragon Age, I like to think that the same thing is going on, except the 'real' quote is never spelled out in-game. So, even though two very different PCs on two very different playthroughs may both pick the same option in a given conversation, I can imagine each of them replying slightly differently, albeit to the same effect, based on the character personality and background. Since my role-playing options already have to be constrained by a handful of branching options, it's nice that I'm not limited to having my PC utter one of three or four specific sentences. Instead of picking which I like best given the other options, I can imagine how I think my PC would react, then pick the most appropriate option for that reaction.