Why would it need a 22-250 specific magazine? It's a 308 based cartridge, it should work in a standard AR-10 style magazine.
Agreed you don't "need" a 22-250 specific magazine.
That being said, the 22-250 is more of an intermediate sized cartridge. It's somewhere in between what would fit in an ar15 and an ar10. It is much shorter than the rest of the 308 cartridge based calibers and has more taper than the rest of them.
Anything I've read on the subject (yes, no first hand experience) suggests that the 22-250 won't feed more than 4-5 rounds from a standard SR25 pattern magazine trouble free.
Now that shouldn't be an issue in Canada because we're typically limited to 5 rounds anyways. The 10 round pistol mags could be problematic when loaded full but if it were me I couldn't see myself wanting to blast away my 22-250 ammo by the pistol mag full at a time anyways.
So yes, I'm sure the expensive 22-250 specific mag isn't really a "need" to be able to take a shot or two at a coyote.
As far as the function of the cartridge in the platform itself goes, at least there are parts available for the ar10 that will let you tweek the operating system to (hopefully) function. Lightweight bcg, different buffer weights, different buffer springs. Unlike my 180-C project where nothing is available off the shelf and I'm still waiting for a place to get my custom made springs done.
It just depends how much money someone is willing to dump into something to get it functioning just right.