I really like how they did it with the King of Red Lions in Wind Waker. He was only around when you wanted him to be. Not like Midna or Navi, who were your constant companions. You could always talk to them and they would help you wherever you were. But with the King of Red Lions, he was only around for the important stuff.
He helped only as much as a guide, rather than a sidekick. The dungeon crawling was done by you, with the occasional help from the King via the Gossip Stone.
He only provided hints when absolutely needed. And if you were ever unsure as to where to go, he would hint for you when you spoke to him, rather than outright telling you (I've noticed this because I am replaying Wind Waker at the moment).
This is the kind of partner I like. The kind that is usually around for cutscenes, plot and the occassional hint or two.
But sometimes we need a partner like Midna or Navi. In a new game (or gaming platform), sometimes we need some extra help because it's new to us. I think that's why Midna is the way she is in Twilight Princess, because the Wii was a new system and well, not everyone was going to get the hang of it right away. I think the partner (oh, come on. We ALL know there will be one! xD) in Skyward Sword will also be this way because of the addition of Wii Motion Plus.
Having no partner at all is kind of... boring, to me at least. I highly dislike the lack of conversation, plot and such because the early Zelda games don't have a partner like the newer games. Not to say that the older games are rubbish, because that's not my point at all! What I'm saying is that though partners make the games a little easier, they also add overall character and plot to the game! Without them, it's just Link, a mute hero, running around slaying monsters and completing dungeons. The only plot developement is few and far between because there is nobody to talk to at any time! No one to help if you're completely stuck, and have no idea where to go next. The partner is quintessential to Zelda because of the character he or she provides to what would be a very dull story if Link was the only protagonist the whole time. (Like in the first Zelda or Adventure of Link). Even a reaccuring character can be very useful if you don't have a partner (say, Marin from Link's Awakening) the entire game. They add something.
I'm not sure what kind of partner everyone prefers, and it must be difficult to please everybody for developers. They have to make disicions on what to do with a partner, weither he be the Midna, Navi or Kingly type. Sometimes they make mistakes (I'm looking at YOU, Tatl!) and other times they hit the spot (in my opinion, The King of Red Lions).
I think we need partners for the laughs, the plot development and the overall addition of character alongside silent Link. :3
(But these are just my opinions~)
It's not to say your idea wouldn't work, because it totally could if Nintendo wanted it to. But that's just not really Zelda, is it?
I dunno. Interesting idea, I wonder what would happen if they used it someday?