Ok, in memory of Johnny Dankworth, here's how a sketch is like a jazz tune.
Say you're listening to Coltrane play 'My Favourite Things'. He'll start out with the basic tune, and then he'll take it and muck about. He'll take that tune all over the shop, he'll noodle, he'll swoop, he'll throw it over to the piano, maybe the drums will get a solo. For most of the track, he'll do all the things that jazz lovers love and jazz haters hate. Then he'll bring it back. The basic tune reasserts itself and... finish.
A sketch is like that.
I've said elsewhere that a sketch is one idea. It can have as many twists and turns, as many opposing viewpoints and (must have) as many jokes as you like, but at heart it is one single idea. The opening of a sketch sells that idea, gets a laugh, sets the tune. From there on you can take it anywhere as long as, like Coltrane's rhythm section, you have the basic idea backing you up. A sketch can, and should, be as surprising as you can make it but every twist is just a variation on the central theme, an improvisation around your tune. Look at how Fry & Laurie play around with the information desk idea here.
The punchline, then, is the tune reasserting itself. It's the payoff - the ideal finish that the start promised. Everything in the sketch is pointed towards this moment. That's why a satisfying punchline gets such a big laugh - it's a Freudian release moment, with everyone getting there effortlessly at the same time.
Of course, you might not like punchlines. A lot of people think they're old fashioned. These are people who have to put stings between their sketches to cover the lack of laughs. A punchline doesn't have to be a badum-tish gag, it shouldn't inspire a wah-wah-wah from the trombonist. It does have to tie up the sketch. A sketch always has to have a last line, obviously, so why not make it funny? Otherwise you might just find your producer cutting out on the last big laugh.
So there you go: Thesis, Antithesis, Conclusion. Oh, wait, no. That's why sketch writing is like A Level History essays. I think my basic point is this: I like jazz.
Well, its just a bit-of-fun theory, thought up over an idle hour on the tube reading Newsjack submissions - and anyway I'm more Ornette Coleman than Wynton Marsalis, so feel free to go your own way, play whatever tune you like.
Which sounds like as good an excuse as any to listen to this.