If a guy is willing to cut their huntable range to respect the limitations of their underpowered cartridge, then there's really nothing wrong with hunting coyotes with the 17WSM. I started hunting coyotes as a kid with a 22wmr of my uncles (previously my grandpa's) and in the last ~25yrs, I've killed dozens of them with 22LR rifles and even pistols. Get a dog at 25yrds and ventilate his clockwork and he'll drop where he stands. There's no argument that it's an impractical calling rifle, since it's so range limited, but I've done so - 100yrds or less...
It's a lot more rifle than a 17HMR, but it's not in the same class as the centerfire 17's, let alone the "standard fare" 22 centerfires.
I have a BMag, a heavy stainless model, bedded into a Boyd's featherweight thumbhole, and re-knobbed with a Glades bolt handle, re-capped with a post-recall bolt cap, with a 4-12x40mm Nikon Buckmaster on top in Leupold Rifleman (cheap) rings. In my wife's hands, it'll put 8 shot groups under 3/4" from a rest in the absence of wind (local indoor 100yrd range).