It just depends on how it's done.
Skyrim gave us a nearly-voiceless protagonist but it didn't make me care all that much about my character. I enjoyed the story, but I focused on everything else around me and didn't put a whole lotta thought into my character aside from the basic stuff. This is mainly because it really doesn't matter who you are, because being the Dragonborn is all that counts. If you joined the DB and killed for fun, or stole for the Thieves Guild, etc. it didn't matter - 'cause no one brought it up and if they did it was to no avail 'cause as long as you 'killed' the big baddie at the end everything was okay.
Origins also gave us a voiceless character to play but your choices actually mattered. If you didn't want to lose certain followers or groups of people you had to put some thought into what kind of character you were going to play. The fact that people reacted to you made me care about my character.
DA2 worked because Hawke was fun. They wrote him well, picked a great VA for 'em, and even though the game suffered in many areas it got the main figure right - so that helped. If more games were to give us Hawke, Ezio, and characters like them then I wouldn't mind. However, if I'm forced to play a boring or awful main character - like that scrub from AC3 for example - then I lose both the ability to make my own char and the experience of playing a well-written pre-determined character, and I'm not a fan of that.
Inquisition was meh, in this regard. Yeah I got to make my own version of the Inquisitor, and we were given a few different ways to respond to this and that, but because they tried to blend the two together (or at least that's what it looks like they tried to do) it ended up being underwhelming. I didn't get as many (varied) responses as I did in Origins, and at the same time there was no way of making my character as interesting as Hawke - regardless of the fact that he was voiced and had a preset role in the story. He ended up being forced into a very specific role and you couldn't really act outside it. Even if you tried to be the biggest, most evil bastard ever or the most witty and hilarious fool in Thedas, you only lightly grazed those edges 'cause the Inquisitor is intended to be some wannabe Paragon with a neutral personality and there's very little room to change that.
TL;DR - If they're as fun and interesting as Hawke and Ezio, bring 'em on. Otherwise, I'll take my voiceless protagonist with varied response choices and go.