It really depends on the animal. Some, particularly feral hogs, are invasive and incredibly destructive. Humans set them loose, so it's our responsibility to run some damage control.

Maybe my area isn't rural enough, but isn't that what animal control officers are for?

Federal and state employees use a wide variety of techniques to control feral hog populations, but feral hogs are very prolific. A mature female feral hog can have two litters a year and as much as a dozen piglets per litter. Because the problem is so severe, the general public are often encouraged to help.

Cattle mostly. These are rural farmers who are looking after livestock / crops