The fact is that Link is all we know, even though there have been variants, essentially, he's still the same Link, that young hero dressed in green.
I can see that Nintendo have tried to differ between Links somewhat, more story focused games have lead to Link's character being more apparent, so I guess we could see that the modern Links have been unique to one another, of course to an extent. However, the idea of having "no" Link is an idea that I've been considering, it could work, it will turn heads, but it could mix things up.
No matter what, we will always see Link as that's made guy, he may be in another split in time separated by a hypothetical universe and by thousands of years, but still we can relate him to that same hero. Now take Link out and you have one of the most iconic figures in gaming out of his origin game -- seems like a bad idea on paper, but I have away which it could work.
One example that I think fits what I'm thinking is Assassins Creed. Here we have multiple iconic figures, arguably two, as the others aren't established by general consensus. However, still you have more than one iconic figure but they're descendents to each other, so they are still connected in that sense, but are two different characters altogether, this could work in a Zelda game in my opinion.
Of course this is heavily controversial, the majority certainly won't like this idea, just look at how the Sonic community raged due to a change in eye colour, I feel it's too big of a change to Nintendo to consider. If we're talking it's effect on the game though, then it doesn't necessarily mean bad, it might be for consistency's sake but a "new" character could bring something unique and diverse. One thing that's more vital is the actual effectiveness of that character, if it's not then what's the point? This also applies to Link as well, so summing up, I feel the definitive factor is not if it's Link, it's his actual character and the effectiveness of it.