I used to live in a cat house, with over a dozen of them, and the feline owner, now moved elsewhere, treated the cats as her children. They were free to be inside or outside cats as they chose, thanks to a cat door. There were no coyotes and some cats acted as predators. Others brought live rats into the house as their own pets. We went into a "rat rescue" mode.
Some sympathy for the dead cat is reasonable, but that does not detract from the great photography of a coyote's successful hunt.