Well obviously you arn't going to compare a .357 to a .30-06, but, you don't need a .30-06 to take down a coyote. If you want to start comparing like that I might as well take the biggest rifle I have, since I am going to all the trouble of carrying a rifle to begin with; I am sure the .338 Win Mag will knock down a coyote.
I own a whole pile of rifles in various calibers. I use different ones for different purposes. Sometimes I use one just because that is the one I want to use with no logical argument behind the decision. In this case, the .357 is more than enough rifle for the game hunted, why should I carry more ? By the same token I have taken out much bigger rifles in search of coyotes just because I felt like it. I called in and shot a couple coyotes with a .444 Marlin. I have shot coyotes with a .25-06. I didn't need that kind of power, but that day it suited my fancy.
Why buy a .357 carbine at all ? Well, it is fun to shoot. I already handload in massive quantities for that cartridge; I buy the brass, bullets, and powders in quantity, I have a pregressive loader set up to load that cartridge. And, for me, the idea of having a carbine and a handgun in the same caliber makes plenty of sense. I take trips out into the back country of Nevada and carry a gun. I like to only have to take one cartridge. I like to be able to have a belt with cartridge loops that I can use with either gun.
I wouldn't hesitate to use a .357 carbine on deer for that matter. It is plenty of gun for deer.