Well then why hasn't Link been replaced with a Mii by now? Only way to truely 'link' with Link is that he'd be as similar looking as yourself. But no, people have grown to love Link for what character he is. I doubt that can be easily replaced with a 'female Link' and get the same results. In which case, I think it might be better to have a character that is also well-known in the Zelda lore. And outside of Zelda, Impa is easily the best option.
You're not getting this. Have you ever read a book?
When many people read the Harry Potter books, they don't imagine Harry Potter as a separate character. They imagine him as... themselves. They imagine they're the wizards holding the wands, casting spells and shirking off homework. They're imagining that they are the toys of Dudley, the owner of Voldemort's scar, and the Master of Death.
Imagining that you're someone that's not yourself is a lot easier when you get to access their thoughts. With video games, you don't have that liberty. But a sense of immersion: Even when the character you're playing as has a voice and a personality, is still possible.
Link serves as this link. He never talks. He has no past to speak of, at least in most games, and what pasts he has can easily be assumed by the player. He is simply a slate on which to draw on, and even in third person it's easy to immerse yourself and subconciously think of him as... you.
With Zelda and Impa, it just wouldn't be the same. They have always spoken. They knew how to speak, and they've always been much more defined then Link. Sure, they could make them silent, but that would not only kill the character, it would have an effect on surely the developer's, and quite a few players, from the backlash of Link gaining a voice's, experience as a whole.
Imagine you're reading the Harry Potter series, but it stars Neville. You still have this hero with a scar and a lack of parents, but he's significantly more bumbling, in need of even more character development. That wouldn't draw off readers as a whole, but it just doesn't fit within the magical setting, the fantasy setting, the life you wish to live. That would wall of a lot of potential readers.
So, let's say you were playing the Legend of Zelda. You were hoping to play as the kid with the Triforce of Courage, mountains of items, and the Master Sword. Suddenly, you play as a ninja.
While that may be alright for some people, is that truly what the dev team wants?