I do not think that Link should have a voice.
The big part about Zelda is that you are Link (or [insert name here], if that's what you prefer). I can play how I want, and do whatever I want when I want. Nobody or nothing is contradicting what I do because there is no "set in stone" character guidelines, other than you wear green and such. Other than that, the character development is 100% up to you. You can choose to rush through fighting evil, or you can choose to do everything else. (You can also choose to only do sidequests that gain you rupees and not do anything else but that would only be a short and boring game.)
Dialog options would be a halfway decent alternative, but only in a very limited sense. In a good RPG they have a varied enough choice that you can essentially get the response from the other character you wanted, and with a little practice and experience you can essentially "choose" an option to get the response you would have gotten by "saying" whatever you want to say. However, this only works with games based heavily on character development and not story or gameplay. (Hence, an open RPG.) Zelda lets you develop your character however you want, if you want. If you just choose to play the game as a game then Link will remain nothing but an emotionless extension of your own self in the game, and that's fine.
When you throw voice overs, it multiplies the potential problems exponentially. Just given one choice of what to say, and you can't "say" something other than what you "choose". And even if it's exactly what you'd say, it's not ever going to be how you'd say it. How would the game know if you like, dislike, love, hate, distrust, etc. the character you're interacting with? Should you put the emphasis in the sentence "Where did you go?" on go, on you, on where? Should it even have emphasis? There is no possible way to get the voice acting from the character you're playing to match that which you want him to be. Meaning the character's personality is predetermined. Which is purely an RPG; not what Zelda is about at all.
It is not a Zelda element to play the character, but rather to be the character. It is not an RPG element to be the character. An RPG, you are playing the character (it's even directly stated in the genre name; you are playing the role). In the unique, amazing adventure that is Zelda, you are Link. And the series wouldn't necessarily be ruined by voice acting alone, but you cannot add something as drastic as voices without changing other stuff, and in that case you might as well not call it Zelda.
As a comparison, look at the Halo series.
I can play that game all I want. But no matter what happens, I will always be playing Master Chief, instead of being Master Chief playing the game.