I've always been under the opinion that pun threads are awful. I love a good pun, but they shouldn't go past the 2 reply 99% of the time. It's rare the 3rd reply has anything funny to say, and past that it's usually just stupid af.
Like with jokes, I don't so much mind the existence of such threads so much as the fact that they are short and easy to both create and digest, which means they get upvoted more quickly and rise to the top.
New users need to know this and stop upvoting low effort comments by default. I don't know if there's any way to enforce this, so it's a cultural thing that only peer pressure from other users can affect.
I have to say, I loved when you would see some great drawn out thread, with each comment being an ad lib of some song, I always thought those were a lot of fun