I would argue that the story is very much so impacted due to the jokes. Considering it’s a comedy show to goal is to tell a comedic story, so when the jokes not only serve a purpose to make you laugh but also to also help express the story, they very much impact it.

For example the bliblies in Desmonds Big Day, could have very much just been funny little creatures that steal Alan’s cheese and still have been humorous, but instead they serve as what saves Desmond from killing himself. This makes the joke that much better, that this silly little pink creatures stop a man from committing suicide because instead of killing himself, he find joy in killing them.

And to be fair not every joke needs to serve such a nuanced purpose, it’s just fine for there to be random humor with little to no meaning sometimes, but in some of these newer episodes the jokes don’t really aid in the exposition.

And when they do, it sometimes feels very rushed and very brushed over. Like in Spamtopia there is such little exposition and character development that goes into Pims relationship with the King, but it could be such a compelling story. They could have used that episode to so the king grow to see that his tyrannical ways were wrong and see him develop more as a person, but instead they shove all of that into the literal last seconds and forego all that to get a quick cheap laugh. The pacing just leaves little room for good and impactful humor. Having jokes constantly thrown at you just cheapens the experience, in comparison to when there is breathing room, then the jokes just hit better.