I'm not sure I'm following you here with regards to the apparent removal of dungeons. Are we not counting the Divine Beasts as dungeons now?
Of course not. They're part of the underworld, sure, but dungeons are a specific implementation of the underworld. Divine Beasts don't follow the same formula as dungeons and don't even remotely play like them.
The only thing missing from the traditional Zelda formula is the gaining of an item and the unique aethetics.
So basically the core element that separates a dungeon from any old cave. The unifying world for this is the underworld. And there are plenty of ways to implement it, with many games implementing it in different ways. Other games have their own forms of dungeons as well, but they're hardly comparable to Zelda Dungeons.
Sure, they're a different style of dungeon, but they still took just as much resources to create as a typical dungeon, especially with the introduction of more physics based puzzles which I can't think of any examples of in any prior game.
Except the developers explained the reason why they resorted to physics puzzles is because they're much easier to implement. Not surprising, since the puzzle is basically "do the thing, we don't care how, we're not going to prevent you from breaking this."
They are such by very definition in video game terms even outside Zelda.
Again, you're thinking of the underworld. And yes, different games have different ideas for what dungeons are. Zelda has its own formula. BOTW doesn't follow it. It doesn't even try to claim they are. Because they're not. And there's no sense in getting hung up over specifics, because I think you know what I'm referring to. You can call them whatever you want. Divine Beasts, Temples, Buildings, Dungeons, etc. but they don't follow the dungeon formula and aren't comparable to the dungeons founded by LoZ, which is the problem.
I've been out of the fan forum scene for a while now. However, after SS, the majority of the community was eager to lose the linearity. Linearity serves a purpose in that it allows tight control over how a player progress. That good if you're going to use it for specific purposes. Games like Uncharted couldn't function without it. Zelda has never been a series that DEMANDS linearity as their development process is the wrong way around for it. Story always comes last.
Story doesn't need linearity. In fact, non-linear games tend to have a much deeper focus on story and lore. Look at the Open World genre, it's one of the most (if not
the most) story focused genres in gaming and it's also the most non-linear. Linearity allows for dungeons to build off each other and when you try to make the game more non-linear, the item usage becomes much more predictable and you're left with lower quality dungeons where the player is less likely to get stuck, as seen with ALBW.
Games like Super Mario thrive off of non-linearity, because restricting Mario limits his platforming abilities and hurts the platforming based gameplay. Meanwhile Zelda has always had a focus on gaining power through item progression and progression works better under a linear setting. The secondary focus (introduced with OoT) of puzzles also benefits from linearity. Without linearity, developers have more limitations on what items can be used, in the case of BOTW, the puzzles themselves and inferior and broken.
Choice and freedom are the main benefits of non-linearity. Open World RPGs benefit the most from it. But Zelda, even in its most non-linear form, doesn't make use of this at all. I'd even go as far to say that BOTW is the most restrictive Open World game I've ever played, next to Xenoblade Chronicles. Zelda rarely offers choices and when it does, they are almost always insignificant. This is most clearly seen with BOTW. Your choices are basically limited to what region you go to first, and it doesn't matter. The shrines from Hebra give the same reward as the shrines from Faron. The Korok Seeds have the same puzzles and same reward regardless of where you go.
If non-linearity is to be used, choice and freedom should be capitalized on. But it isn't. Because it's outside of Zelda's element. And if they were to capitalize on choice and freedom, they would need to fundamentally change what Zelda is. And why do that when they can make a brand new series instead?
Also SS was less linear than the previous titles, so I don't see what its linearity has to do with anything. It's the first 3D game since OoT that lets you do anything out of order. To be honest, one of my main gripes with BOTW is that it follows too closely in SS's footsteps and made a lot of the same mistakes.
OoT's Hyrule field was a non-linear environments and people still praise it. WW's Great Sea was a non-linear environment and is still my favorite part of that game.
What are you talking about? Hyrule Field and the Great Sea have gotten a LOT of flack. The overworld has consistently been the most hated element of every 3D game for being too open and barren. Meanwhile the 2D games didn't have this problem until PH came along, made the world much more open, and people hated it.