The issue is that it would be very very expensive. Think about it, the game doesn't just have a standard 1 male and 1 female. Different races may sound different, and then we add in Origin characters (I dislike origin characters as PC but it's in the game). They would have to record every single companion character being used as PC on top of standard customized character.
This isn't the 90s anymore, it isn't some hardcore difficult thing to do. As a matter of fact, for the majority of modern RPGs it is standard. When the origin characters record their characters lines, they then record the PC text. Then it is chopped up and assigned to certain variables (like if the origin character is playing as a PC). You seem to be insinuating that they would have to have multiple VAs for all of the origin characters and that is so much more difficult, when in fact, they already voice EVERY OTHER CHARACTER in the game, besides the PC.
I mean I get it, it is not something you want, but don't act like it is something super difficult to do. I mean you can even use filters to change up tone and base of voices to use them for different characters. A lot of voice actors can in fact do a few different accents and voices to begin with. It is not uncommon.
Funny, you seem to make an assumption on what people prefer even without them telling you. I actually love to have voiced protagonist in general over silent ones, but I don't see it as something feasible for this type of game. Yes, it is something that is tough to do as the number of voiced dialogues would be very high. Voiced companions and voiced NPCs are set and limited while for PC, there would be multiple voiced for branching tree, each character you interact with, and a whole bunch of things that are crossover in these dialogues like Shadowheart could have half elf's voice on top of her own dialogues. I don't think you realize the amount of work it has to be put for all of it to work. I recognize the amount of work and how expensive it could get just to get it to work and it would be better spent for other things, so nah, DAI already has a huge issues when they try it and they only have 2 voices for each gender. It seems like a trap that eat up development time.