If we are going to bypass the "worst TYPE of puzzle" question, and just point out the single puzzles that were the worst in each of our own opinions ... then here's my list (in no particular order) that I found to be horribly difficult and annoying:
1. I can't recall exactly where it was, but it was one where you had to push a rock to get it going down a path and have it end up in a hole in the ground. This particular one had the "hole" in a spot where if you missed, the rock just kept rolling and ended up going off the edge of the hill. The "path" was not well defined, and the boulders didn't really like to follow it all that well. I think I got lucky on something like my 20th try and the rock didn't go off the end of the hill at the bottom. I was then able to use stasis to knock it into the hole. That one had me as frustrated as can be.
2. The one at the northwest "corner" of the Gerudo Highlands where you had to basically drop a boulder off the high part of a cliff and have it land in a hole below. Getting the boulder/snowball to fall perfectly here was damn near impossible. I had to do that one about 12 times or more before I got it. The real pain for the puzzles like this one is the waiting for the snowballs/boulders to return to the starting point so you could try again.
3. There is a puzzle in the Faron area where you have two boulder on a chain, and you have to get them both on top of some rocks in the stream. I don't think it's possible to do it w/out using stasis to hold one on the rock while you do the one on the other end. It took me forever to realize you needed stasis to make this one work, and I was about to rage quit the game prior to that. It was actually my wife who suggested stasis, so I owe her for that one.
4. Not all of this "type", but the apple trees where you have to make all three trees look the same. One of them (can't remember exactly where it was) always had rain/lightning, and it kept striking the trees, ruining my ability to even attempt the puzzle. Then, finally the game decided to have good weather there, but it took me days (real time, not game time) before the trees and apples were all back so that I could try again. I completely blame Nintendo for that ... making the regen time on a puzzle like that last so long is just cruel.
5. The puzzle at the northeast portion of Lake Hylia where the Hylia river has the water fall into the lake ... and you have to pick up the block on the east side of the waterfall, and get it into the puzzle on the west side. I was able to do this, but I feel there MUST be an easier way than how I finally got it.
(EDIT TO ADD THIS: Yes, the korok puzzle in Lurelin Village where you had to get a rock on top of the house ... that was just painful and unnecessary if you ask me. I don't mind the puzzle being a challenge, but the real challenge should be more about simply identifying the existence of a korok at a given location, and it should be FUN to "solve" the puzzle and get your reward.)
Now that I have those specific ones out of the way ... I THINK I know why there are so many koroks in this game ... which is simply to make sure there are tons of them everywhere, and each person can find the ones THEY find, and get enough to at least get close to fully upgrading their inventory slots ... if not fully max'ing it out. However, 900 is just too much, period. And because of that, having to basically check under every rock, inspect every inch of where you go for leaves, or holes with boulders nearby ... or stumps to stand on and race to a new location ... etc. It's just too much in general, and wears you out if you want to find them all.
I'm not sure what the answer/solution is ... but man the whole korok thing in this game is just brutal and mentally draining. It's so fun to cruise across the landscape from point A to B, for whatever mission you're on ... and having to take it painfully slow takes a lot of fun out of it for me. On the other hand, if you just ignore the koroks during those times, and then go back later on a dedicated mission to find them, well ... that's just more tedious and mentally exhausting.