I've seen coyote tracks around a carcass but nothing to indicate they eat dead coyotes. Buzzards and ravens chow down on them as well as golden eagles. I've seen that. I caught Javelina on a carcass.
As far as a carcass spoiling the area???
An emphatic NO!
In the old days it was thought that a carcass would keep other coyotes away. That is the reason you used to see them hanging on fences years ago.
When I find a carcass, I pay it no mind and start calling.
A carcass is indication that there are coyotes around. When the food source depletes, that's when the coyotes leave. Pressure can do this too, but is the food source is still there, the coyotes will retun a few days later to set up house. The good thing about educating coyotes is that the forget.
I've taken coyotes in areas where the ranchers were using coyote getters, so there were many ocassions where carcasses were scattered about and that never stopped a coyote coming to the call.