Lets examine some analogies. Is it over-kill to use 80# test line and a wire leader to catch crappie?,no, it won't catch them any better than 6# test with only a minnow hook.It will catch fish, it's just more than you need.
Is it over-kill to use a 100# pull long bow and broomstick sized cedar shafts to bow hunt rabbits?,no, it won't kill a rabbit any better than a 50# compound bow using light carbon arrows.It will kill a rabbit, it's just more than you need.
Is it over-kill to use a 10 ga. double gun with #2 shot to hunt bobwhites over a dog?,no, it won't knock down a bobwhite any better than a fine 20ga. or 28ga, O/U using #7 shot. It will kill a bobwhite, it's just more than you need.
To most hunters, it's about matching your rifle/cartridge to the size of the game.Is it over kill to use a 270 or a 300 mag....no. Neither will kill a coyote any more dead,than my .17 remington,or someone elses .20 tac. or .223, it's just more than you need.
The coyote is on average, a 25-30 pound animal, it just doesn't take a whole lot to kill one with a well placed shot, from what most of us consider predator calibers, such as the .22 centerfires, .17s .20s and .19s.
When they get shot with the big stuff, there is usually a big mess. Leaving a lousy hide if your keeping to skin,and an even uglier corpse if your just after the glory shot with the Cannon then kick the carcass in the ditch kind of guy.
You'll see more positive comments about photos, when they are posed with coyotes or cats, that just look like they went to sleep, than you ever do when the bodies look like they were hit with an RPG. Im sure there is a small percentage of guys who get quite tickled when they blow up a coyote like a prairie dog hit with a 22-250, in fact Ive seen it right here. I don't understand it, but Ive seen it.
So, is the .270 overkill; no.....it's just more than you need.