Seems like something out of a DC or marvel Multiverse (If you know what I mean ;D). Honestly, NO thank you. It sounds great on paper, like Van said, but it wouldn't work out in my opinion.
First of all: this ^
and @AnimeHat: It IS a good idea! I just don't that it would work. Consider all the programming the big N would have to. How many Link's are there? That means programing 14 (or.. whatever the number of Link's is) different worlds, that are basically the same thing, just matching their respected Link. I think the game would be really confusing, not to mention all the paradoxes... oh man... But as I said, its a good idea on paper, just a little difficult in reality. Or maybe I am just over thinking this...
One more thing, it worked in Sonic because he met his younger self making it only two of them (I still say there is only one Sonic but, that's an argument for another time). I don't think it would work in Zelda due to how many Link's there are and the fact they are all different incarnations, it just does make sense :/. As stated before.