I think the "rimfire for coyotes" quote/unquote debate is very similar to the cartrdige debate for hogs. There are guys out there that have been knocking down hogs for generations with small caliber, small cartridges, with well placed shots behind the ear. Then there's the other half that treats a hog like any other big game, taking vitals zone shots, needing a heavy 30cal to punch through their fatty, gristly shield. Both work, but you hear the 30cal guys knocking the 22cal guys year after year, saying they're undergunned.
But it's hard to argue with dead hogs...
For coyotes, there's the 22CF guys that keep preaching that no RF is big enough. In my experience, if you ask these guys where to shoot a dog, again, they revert to their big game mentality, "shoot em in the vitals". It's a no-brainer that a .17HMR won't likely penetrate and produce an exit wound on a dog at 300yrds, but nobody's talking about that range. At 100yrds, putting a 17cal hole through a coyotes skull or heart is child's play.
At the end of the day, it's hard to argue with dead dogs...
So ultimately, there's no denying both work (22CF and mag RF's, even .22lr's occasionally).
It's hard to not have at least a mild case of "magnumitus" when we've been exposed to it for so long. If we look back at hunters that "used what they had, and it worked!" stories, you'll see tons of tales about Bell's elephants, or the .22 Hornet being used for polar bears, or Teddy and his .30-06 making a trip to africa, etc etc. We're so used to blowing exit wounds out the back side of animals and over powering game, we forget how little work REALLY needs to be done to take one down.
A bullet through the heart or brain will kill any animal on earth. A .17HMR or .22WMR (or even a .22LR) can push a bullet through a coyotes skull or rib at 100yrds, and most shooters with modern rimfire rifles and good optics can place a bullet inside 2" at 100yrds. If it has the "stuff", and you can get it there, odds are, it's going to do the job.
And it's dang nice dropping a single X-stitch closing up a single 22cal hole in my hides, rather than "footballing" out a golfball sized exit wound.