I beat all the Divine Beasts.
Nintendo obviously wanted to completely reinvent the Zelda conventions, and it's interesting to see that they went this direction with the dungeons. I think most people were not really clamoring for dungeons to be dramatically altered. Many enjoyed the dungeons in Twilight Princess and Skyward Sword, even if they weren't keen on the game overall.
I really enjoyed them, though some were better than others. I often hear that they are too short, or too similar, but I disagree. Yes, your time inside the actual dungeon is shorter compared to other titles, but the whole quest line to get in the beast, and heck to actually traverse the landscape to get to the city in the first place, are substantial. I think if you just visit the city, then warp back when you want to tackle the dungeon (which I admittedly did with all of them), it does make the journey seem a bit less epic since it seems like it boils down to "Ok I'm ready, can you give me a ride?" I thought the aesthetics of the actual beasts were really cool, so I didn't mind that they lacked an elemental theme interior.
They do manage to reflect the openness of the game as a whole. The terminals do not have to be accessed in a set order and you are given free reign to manipulate the beasts early into the dungeons. They encourage experimentation and problem-solving similar to the shrines. Though like past dungeons, each terminals basically have one solution you have to figure out as opposed to the free-form solutions you can create in shrines or in battle. The previous Zelda dungeons are the very definition of lock-and-key, where you cannot progress unless you have done a very specific thing in a very specific order. You know how far you are by what items you've obtained (you get the map, then the compass, then the item, then the boss key etc.).
My main criticism is the lack of combat in them. Zelda is known for its enemies and bosses, so it's so strange to see these beasts almost completely vacant. I think they could have done a lot, like having malice-infested or guardian versions of existing enemies. The Master Sword being super powerful, while cool in a story sense, makes the bosses way to easy. Speaking of the bosses, while they were diverse in how you battled them, they all looked way to similar. Think of the wild designs in past Zelda bosses. This time it's just goop with a guardian weapon and Ganon's haircut. They seem so uninspired when compared to everything else in the game.
I feel like there's a lot to like about these dungeons, but they can also be improved upon. I would like to see the more open aspects of the dungeons retained, while also incorporating more traditional elements like distinct enemies and more elaborate puzzles.