Definitely in favour of a voiced protagonist, here. You can complain that it ruins your immersion and that you can't project yourself so well onto the character, but, first, I had no trouble projecting myself onto Geralt and he's an established character who occasionally lets the player decide his morality, and second, a mute protagonist just makes you a spectator in everybody else's stories. Let's take Fallout 3, for example. The Lone Wanderer is the protagonist, but since he's a total mute and simply cannot project any kind of character beyond what the player is feeling, it's less of his story and more of his father's colleagues' story. The Wanderer just opens doors and shoots mutants while everybody else does the emotional heavy-lifting.
The same goes for Skyrim. Sure, I'm the Dragonborn, but it's Delphine and Esbern who undertake any actual plot. I just kill the dragon they tell me is the one that needs to die. It's exactly the same in the Civil War plot. Sure, in my head I can say, well I joined the Stormcloaks because I was almost executed by the Empire and took it personally, or I joined the Empire because I believe they're what's best for the region, but ultimately, Ulfric or Tullius point at a camp or a city and I clear out all the mooks so they can come in and have their story told. The siege of Whiterun isn't about the Dragonborn single-handedly taking on a city. It's about Jarl Balgruuf's noble attempt to remain neutral in a horrific conflict ending in tragedy. No matter which guild you eventually become chief of, the story isn't about you no matter how many times they call you the 'chosen one.'
You can see it most plainly in the difference between Dragon Age: Origins and Dragon Age 2 - and I'm not talking about gameplay or even dialogue variety because both are irrelevant, and I'll explain why. Origins had multiple origin stories, but for the sake of the plot they all had to end badly so you would have an excuse to join the Grey Wardens. If you're a human noble, your whole family gets wiped. Your character does not care so much, because, beyond saying "I'm really upset because my family died," there's only so much selecting a line of dialogue can convey. There's no tone, no inflection, and only what the player imagines it sounds like, and since video-games are intended to give our imaginations form, that seems a tad redundant. As a result, though, you remember Alistair, you remember Morrigan, and Wynne, and Sten and all that lovable bunch because no matter how many lines of dialogue you are offered, you're always going to be upstaged by the wit or eloquence of somebody who actually has a voice.
Dragon Age 2 suffered a little less from this problem because you could hear Hawke. S/he spoke. Sure, maybe you were disappointed that every conversation boiled down to Diplomatic, Sarcastic or Aggressive outcomes, but I didn't really see much more variation in Origins. Especially not when it came to choices that mattered. I, personally, enjoyed conversations much, much more when they had two voices, rather than the one-man interrogation Bethesda games specialise in, because they actually sound more like conversations, and less of info-mining.
If a game's world is convincing enough and the protagonist's voice actor talented enough, you could be playing the most linear game ever and still feel invested and immersed. If Fallout 4 does this well enough, the protagonist can actually be involved in the side-quests and the main plot, rather than watching somebody else's story unfold while standing awkwardly by the door. You might have liked Veronica a lot, but your character stared gormlessly at her and gladly put her life at risk while unblinkingly mowing down bad guys and monsters, and then recited some unconvincing compliments.
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