I can't remember the source, but it was probably "Eric in the evening" the longtime jazz DJ on WGBH Boston who taught me Monk was the most recorded American composer. I read so much expository writings on jazz it could have been anyone. So I do not have a foot notable source to site on that, my mind is only half a steel trap.I think one can make just about anything groove, it's just a matter of how it's approached. "How High the Moon" was a popular song without a strongly pronounced groove to it, but it certainly lends itself to being played with a groove ... and of course, Parker's "Groovin' High" rides on those changes.
I wasn't aware that Monk was the most recorded American composer, though I certainly think of him as widely recorded - do you have a source for that? I know Gershwin had a ton of very frequently performed songs, and "Summertime" in particular was massively recorded. I might've guessed him, though it's not something I've really looked at.
Some standards were born to swing eh? "It don't mean a thing if it ain't got that swing".
I still greatly prefer Purpose Built Jazz compositions, like the Herbie Hancock album Maiden Voyage. Maybe that will be my shower music today???