Spinners, as they are called, are very common on predator hunting shows.
I kill many coyotes, yes it's fun, but the main reason is: they are brutal killers. Once you find a prized animal that you helped bottle raise with its guts strewn about, you stop admiring their beauty real quick.
The fact of the matter is, coyote populations continue to grow as we make more favorable conditions for them to flourish.
Coyote and pig control has no place for sportsmen.
That being said, I have never had a "spinner" because I will never take a long shot on them. Coyote hunting for sport is about making long shots. I tend to get close to them to shoot them. I shoot near livestock, so missing is not an option. Many coyotes suffer from mange so killing them before winter is doing them a favor.