Totk/botw dungeon divide between fans is super interesting isn't it? I think everyone is right here, they aren't "zelda" dungeons, and zelda as a series has lost a certain something with that move. But also people really love the new direction, especially the shrines in totk.
For the items, you can see the lineage directly from A Link between worlds through to totk. In albw they were super proud of their "get any item as soon as you want by renting any one item" system instead of having to beat a dungeon to get items, it let you clear the games dungeons in (mostly) any order you wanted. In botw they gave you all the items all the time, that killed progression entirely. But the build your own solution idea in totk seems to have brought something new. It'd be hard to go back to dungeon items without losing that aspect of totk.
I'm not massively confident that Nintendo care to close the gap on dungeons though, they seem happy with the way things are now, there's a case to be made that the actual dungeons in totk are a lot less interesting than the divine beast dungeons in botw.
Do you think there is anything lacking in botw1/2 that bringing back items fixes?