I enjoy puzzles in games so long as I don't have to do the exact same one multiple times. Slightly different ones that get more challenging is fine.
I do like the sort you find in zelda or skyrim that have everything you need to figure out right there. I also don't mind if there are basic skill checks like platforming but I don't think an mmo should get too complicated there.
I don't like puzzles that take you all over the world like treasure maps, though. It can get frustrating realising that the spot you totally thought it was taking you to wasn't the spot.
I've never really had any interest in puzzle games. I would probably just play games on my phone for that. That said, basic mechanics that just require some coordination between group members might be interesting - turning multiple keys at the same time, multiple players standing in just the right spots with mirrors to shine light on a trigger point, etc.
I think that, while puzzles *could* be done in interesting ways, they could also lead to either frustration (either from tedious trial and error or some penalty for trying the wrong solution) or a mere inconvenience, after everyone looks up the solutions online.
Not unless it makes sense contextually. Is there background for it's existence within the lore? Who built it? Is it realistically designed to have been believably built by the world’s inhabitants? It's likely these things would be pretty rare if they did exist.