If the plot starts to intrude, it takes the sting out of the jokes. You can see it when characters start dialogue 'signposting' i.e explaining why the story is going where it is. That can be funny too (Billy Wilder was a master), but Thick of it, from what I have seen, is enjoyed by familiarity with the characters and the situations - it gets better the more you know them. So by plotting to have them do unfamiliar things, it means you lose the familiarity. It's not that Tucker's tantrums are funny, but the fact that you know they are coming and are amused by their creativity. Repeats with a twist. Like all so-called original creativity.

You can't be me, I'm taken