Heard Adrian Edmondson on Desert Island Discs and one of the interesting things he said about comedy was that there were a limited number of jokes all of which he believed are contained in the recorded works of Laurel and Hardy and that he would be able to enumerate and show all of them from those works.
He also said he was tired of comedy as he knew all of the jokes. Later he sort of contradicted himself by saying that Waiting For Godot is a very funny play and that he felt he had not yet understood it all.
So that's kind of an interesting counterpoint...he does essentially conflate comedy and jokes.
I think the word "joke" in the context of his interview was more or less intended to mean "bit" or "skit" or "humour-incitement type" -- rather than literally joke as in "knock knock."
I believe he actually said that all humour is passed on, i.e. that all the comic acts that have come along after Laurel and Hardy were in essence re-enacting scenes that they had performed, in another form, prior.
Of course, Laurel and Hardy were brilliant, but it would actually be naive to think that the chain began there. Performed comedy is as old as civilisation itself, and always fluctuates in sophistication/depth relative to the target audience.
Laurel and Hardy represent a talented comedic duo, heavy on physical humour (though not without wit) captured on film so that the physicality of their performance was not up for debate or a supposition, and was available to be absorbed and drawn upon by later comedic performers, and I think this physicality is why Adrian calls back to them. For him, they offer a textbook approach to a broad category of humour.
As for the finitude of humour, I think it would be rather more bizarre if the contrary was true and humour was infinite. Then everything could be funny. Maybe there are a lot of permutations for humour -- if you think about it, the audience (and by extension the time they live in) somewhat dictate what is and isn't funny, and there are considerations as well for cultural context (i.e. JP and CN are going to have a lot of material that will seem nonsensical to a Western audience and vice versa) some humour is obviously universal.
But even to include all topical, regional humour, the number of phrases and physical movements of bodies that can trigger genuine amusement is very likely to be a finite subset of the possible permutations, especially given that all permutations themselves will be finite in total number (there are not an infinite number of words or possible physical occurrences...)
Perhaps indeed there is even a small number of types of humour-incitement, of which all topical, regional jokes are simply manifestations. To group humour-incitement types in this way, Adrian's assertion seems even more acceptable.
He doesn't say Laurel and Hardy invented humour or anything that we could immediately refute. I think he considers their work to be the textbook. Everything you should see before coming up with your own material can be found in their catalogue.
Like all art, grasp the fundaments and figure out which rules you want to subvert to get your message across, for the sake of doing so rather than empty rebellion or feeding reviewers from a marketing perspective.
Sometimes there's no reason to break a rule, and sometimes there's every reason.
As for his fatigue, whether the man has had exposure to humour from other cultures is not clear, but certainly in the context of his own culture I would be inclined to agree. The vast majority of comedy in the West is very obviously recycled material with different packaging. That's not to say that sometimes the later recyclings aren't better than the "originals" —- a lot of it is in the delivery, and if you watch them all without bias (nostalgia) you can probably pick out some cases where a comedy from 2007 is funnier than something conceptually similar from 1987.
A lot of people grew up with comedy shows that were the best of their time and thus become the best for those people, and they watch stuff 20 years later after having rewatched their favourites a dozen times as well and it all seems less novel. Perhaps the same effect occurs for the performers as well as the audience.
Adrian also lost his partner in comedy, the infamous Rik Mayall, and this perhaps soured him on comedy without that second half to bounce off of. They used to tour live and they would often break character and break the fourth wall —- while their long collaboration and friendship would lend a good deal of weight to it, as well as topical spice depending on the region, I think they were keen to do it anyway to keep their material a little fresher and keep things interesting for themselves while doing it. Touring the same act up and down the country would surely be enough to convince anyone it's all been done before. Losing that certainly confines one's repertoire to only the rehearsed material.
I think he's married to Jennifer Saunders (of Absolutely Fabulous and French and Saunders fame) but I don't think they ever collaborated much.