Joke generating AI has been an area of research since at least the 1970s — so, around the same time as some of the first planner-and-ontology-based narrative generation systems. There are plenty of academic implementations floating around, for people willing to do a few minutes of research, along with papers on the subject by the likes of Marvin Minsky. I’m also aware of a few dozen non-academic joke generators active on twitter. It’s not terribly difficult to implement one.
The difficult task is not creativity: a random number generator is more creative, strictly speaking, than any human can ever be, and we have lots of enormous ontologies to use as source material. The difficult task for these machines is to figure out how to avoid telling jokes that are too obvious or too obscure for their audience. (And none of these implementations, as far as I know, try to tackle this problem — they tell all the jokes, and then people latch on to the ones they like. This puts them in the same category as professional comedians.)
Before saying that making a joke-generating AI is impossible, I recommend spending ten minutes writing one. You will be successful.