At this point, why don't we just classify coyotes as a pet? Sure, they're wild animals, but so are cats, and we're fine with them, so why not?
This is a really interesting point actually and feeds into similar discussions I've seen on pet foxes, servals etc. The key thing here is the distinction between domestication and taming.
Domestication is multigenerational; it means that an entire species is habituated to human relationships (for pets, farming, service etc), with hardcoded instincts built in through generations upon generations of husbandry. It actually causes genetic changes in the species being domesticated.
Taming is the process of habituating an individual animal to human contact and moderating its behaviour. It doesn't make meaningful changes to the habits, needs, instincts and temperament of the animal. Coyotes, wolves and foxes are canids, but they are not dogs in the domesticated sense, just as servals, lions, cheetahs are not cats in the domesticated sense and to treat them as such - no matter how "tame" they might be - can be a significant cause of distress and confusion for the animal on a fundamental psychological level!
(But also. An important note. All these coyotes are nonetheless good bois)
