Zelda's always been a dog's game instead of cats. Except Twilight Princess for some reason.
Anyway regarding the hookshot, it would fit perfectly fine in Breath of the Wild. Saying it would break the climbing mechanic is like saying the boat/Korok Lead mechanic is pointless because I can glide to that island anyway (or use the cryo-power). The hookshot would provide an alternative to climbing and be of help in the rain. Which can get tedious at times by the way, the rain, and could essentially be part of the bow weapon type where it breaks after a certain amount of shots. I mean this game also features the boomerang in the same way, which I'd actually consider a lot more pointless than the hookshot ever would be.
I agree with most other points in OP, though aren't feeling very strongly about their inclusion or omision either way. I don't agree with music though, like mentioned in this thread. The subtle music with emphasis at particular spots or during certain events is much, much more powerful than continues bombastic tracks like in the old games could ever be. In a game where you spend this much time in the overworld, a looping musical track would actually become annoying.
There's one point I am strongly in favor of; the dungeons. The shrines and divine beasts are cool and well done, but they're no match for the fullfledged themed temples of the Ocarina of Time/Twilight Princess/Skyward Sword calibur.







