Comedy no comedy

Riffing on Banes' newspost from a while ago of "Horror minus horror" http://www.theduckwebcomics.com/news/2017/oct/18/horror-minus-horror/, does a comedy story without the comedy STILL work as a comedy? And does that make it BETTER comedy than something that doesn't?
I would contend that is the case.

Hear me out:
Pure comedy without much story can often be pretty hit or miss. Take gag comics, or prop comedians. UGH! Take them away…
Sketch comedy is the same: Benny Hill sketches https://www.youtube.com/watch?v=isiZ9U83_SM didn't have much story and they're often pretty flimsy, much like the actress's outfits… While in Mitchell and Webb https://www.youtube.com/watch?v=HMGIbOGu8q0, or Fry and Laurie https://www.youtube.com/watch?v=fe9S0TRXGBQ the sketches have a clear story and they're basically pure art. Prank shows and spoof movies like Airlpane are more examples of comedies that don't work at all without the comedy.

In terms of comics we have full page story comics VS 3 or 4 panel gag strips or even single panel comics. The latter kind are less likely to have much of a story, but when they do, even if it's only implied by the audience's relationship with the characters, they're so much more effective. We know a lot about Calvin and Hobbies for example so even when the strips don't have a story it seems that they do anyway. The Far Side by Gary Larson is a great example of a complete narrative in a single image. Even when the art is simple it still works as narrative because we have a relationship with the cows, we know the crabby ladies with their horrible cat-eye spectacles and their suffering husbands. The comics actually become better when you HAVE developed that familiarity with the characters, just like TV sketch comedy can work even better when the same characters appear in multiple sketches.

I'm NOT saying that comedy NEEDS drama to work or that it needs stakes or tragedy or anything like that, or even that story comedies are always great! No, NONE of that is true.
What I AM saying is that if the comedy could work as a good story in its own right even if you removed all the comedy, or we have enough of a relationship with the characters to care about seeing more of them even if we didn't find them funny, then it has a better chance of being a good comedy than something that couldn't stand without the humour: If it has a crappy story like "Meet the Spartans" for example, or something where you don't like any of the characters (that would be "Friends" for me), then it probably won't work as well as a comedy.

OK, now could someone please set me right? :D