I have no qualms with the unrealistic oddity of finding items in dungeons used to solve those dungeons, as I don't attach a deep level of plausibility or realism to the Zelda franchise. To me it generally just makes for good puzzle solving, if formulaic.
That being said I wouldn't at all being opposed to that formula being shook up, and I'd like if you very early on (or at the start) were equipped with the basics. I'm less fussed about "You found a bow in the dungeon that needs a bow to be conquered!" so much as finding the bow in a dungeon in the first place. Not because of implausibility, but because I've done it so many times now that the impact is lost. There's only so many times you can find the bow or hookshot in a dungeon before it becomes a bit trite and unoriginal.
So yeah, I do like the idea of dungeons housing more exotic and original items. This is something I thought Skyward Sword actually did pretty well with. Finding a bombs wasn't an issue, but giving the player the flying beetle and using that as an extension of bomb use was a nice creative twist on an old idea while using a fresh new item. I enjoy that most of all; discovering a new tool that I have to learn and master in combination with familiar stuff.
I guess that's been the bane of a lot of my frustrations with the Zelda franchise even when I'm loving it. I think it's wrong for it to totally abandon certain formula and ideas that form an integral part of its identity. But good designers don't do that with a franchise. You don't need to reinvent something so it no longer resembles its origins. Creative designs can take the formula and reinvent implementation and execution of said formula to keep it fresh. Again, something I thought Skyward Sword did exceptionally well a number of times.
But I can imagine it's a hard balance, enriching your game with an identity that's so strictly based around pacing of item acquisition and use, and at the same time trying to reinvent that. ALBW does a great job of shaking it up, but it did come at a cost to that balance, which others have mentioned above.
I think that self-sufficiency is a big part of the reason Zelda has been struggling with overworlds as of late. Aside from connecting the dungeons together, there is little to no gameplay necessity derived from the overworld. You don't need to "explore" because you are always told exactly where to find the next dungeon. You don't need to worry about preparing for the next dungeon because everything you need to complete a dungeon can be found in the dungeon. This includes health and ammo.
By placing all the necessary resources inside the dungeons, the developers reduce the overworld to a glorified hub. There is no necessary reason for it to exist.
Skyward Sword changed this by having the various overworlds based heavily around puzzles in order to progress and unlock new areas. But even so, I disagree, because I think downtime is an important part of any adventuring video game. There needs to be a break in the pacing that dungeons alone do not provide. The overworld is a bit of a sandbox for you to explore at your own pace, soak in the atmosphere, and ideally explore item use in mini puzzles and discoverables for extra bonuses. I do feel the emptiness and aimlessness of the overworld is a bit too much at times though, and that adding resources to the overworld or more events and interactivity with the overworld would be very welcome. As much as I love the game, Twilight Princess suffers badly from this; massive play space that while arguably immersing is massively unimpressive towards game mechanics
and due to hardware limitations visually empty and often lifeless. Skyward Sword does it well at the cost of (arguably too much of a cost at that) play space and a true sense of openworld "hub". Zelda U will, in many ways, be the real test. The test to see if Nintendo resort to awful Ubisoft-like collect-a-thons and checklisting.