I feel like this is a complaint that only gets leveled at Nintendo franchises because they've been around the longest: "Oh, they've been around for 25+ years, and they haven't changed a bit." While yes, they haven't been masters of innovation within their own franchises, the fact that Nintendo has within its stable a platformer that has spun off into dozens of sub-genres, an action/RPG, a shooter (side scrolling and first-person), an RTS/management sim, and monster-collecting/JRPG is more diversity than most devs have today.
But this isn't the point. And, to use common words to effect a transition, what is the point? What would re-skinning the next Zelda game into something not-Zelda accomplish? At this point, it would be clearly recognizable as adhering to the Zelda formula and story, so there would be no "Wow! This is unique!" moment that you seem to expect. There would instead be a moment more like "Wow...this is...Zelda? Why did they change the names?"
But maybe you're into time travel. Maybe you are curious about that alternate dimension wherein Nintendo decided that Zelda II (Imma stick with addressing Zelda cuz it's what everyone seems to care about in this thread) would instead be called The Adventure of Ezekiel, and every subsequent game that is "Zelda" in our universe became its own standalone adventure in this theoretical alternate instance.
Again, what would the point be? Instead of having an established franchise with its own mythos and immense network of elements to draw from, it would become the Final Fantasy of Nintendo--and if Escapist forums have taught me anything, it's that Final Fantasy and Nintendo combined would coat the world in a thick layer of shit.
In all seriousness, though, it would be like Final Fantasy, but without the benefit of giving each game the same name. Honestly, I see no way this scenario ends in any way other than it has already: the games, despite their ostensible "separate-ness" become treated as a franchise because of their obvious similarities, until eventually Nintendo releases a timeline that establishes that every game shared the same universe, etc. It just makes more sense that way.
But let me tell you about the benefits that come with a franchise with as much history as Zelda: an established universe, with its own mythos (this lends narrative significance to just about every major plot point and recurring character a Zelda game throws at you); a multitude of classic, instantly recognizable musical themes (the recurring musical cues in every new Zelda game get me excited, but I like video game music, so this point might only be a benefit for me); and of course, cachet.
Could I accept a new Zelda game without the aesthetic trappings of the previous Zelda games? Maybe. If Nintendo told us, "Our upcoming game, The Ballad of Wally: Flute Continuum (or whatever) is meant to carry on the torch from our Zelda franchise", I'd probably give it a chance. But again, I'd question why it was necessary.
Wait, are you complaining about the repetition of story elements in Zelda? Most people complain about the gameplay, dude. And considering that Iwata or whoever said they focus on gameplay ahead of story when developing Zelda, I don't know what you were expecting.