I would disagree somewhat.
I think you accurately describe current cultural tastes for humor, but it was not always so.
Punching down has not always been in bad taste. I very much recall when that was the case in my youth. Young people now do not seem to share that sensibility like they did then.
See: Blonde jokes (ETA: tough for me to explain how this one is punching down, but it feels accurate), pollock jokes, “guy with no arms and no legs” jokes, and many more.
As conservatism is really about not changing things at its core, it is no wonder conservative humorists still have a taste for punching down.
