So, this isn't culling because it's necessary, it's just killing for sport. Why is this even legal?
The contests also have been defended as a way to keep wildlife populations in check -- especially for coyotes, which are viewed as livestock-killing nuisances in some areas.
I love how humans always try to justify their shitty acts. There are plenty of groups who have been working with local populations for years, mostly in asian and african countries, to help farmers with predator problems. In africa, they use "bee fences" to keep elephants from fields. India, they discovered that wearing a mask on the back of your head can keep tiger attacks down. There have also been certain dog breeds used to deter larger predators from livestock. Getting creative it the way to go, not pointless killing.
Also, if there are no coyotes to eat the local rabbits, squirrels, etc then they will be overrun with them, and they will make BIG problems for livestock (assuming they aren't factory farms).