Back when we extricated wolves from the US, they had bounties on wolves and coyotes. Every year the population of wolves dropped, and so did the number of bounties paid out. Every year the population of coyotes stayed the same and the bounties paid out on coyotes remained the same. Not only was hunting pressure not effective in lowering coyote populations, but it pushed coyotes into areas that they did not inhabit before. There are coyotes in every single major US city and that was not the case when settled this country. Yellowstone is a great resource for watching what happens with many species let alone with zero hunting pressure. The coyote population in Yellowstone initially rose, then leveled off and has remained the same since (well until the wolves came back anyway).

I'm not advocating that people shouldn't hunt coyotes, only that hunting is not an effective method of population control. Cattle ranchers can and do believe what they want, but hunting coyotes doesn't put a dent in the population. It's pretty much the same with pigs. People who say they are hunting them to control the population are either lying to justify their love of hunting pigs/coyotes, or are misinformed in the effect their hunting is having. Again, I don't care either way, just pointing some things out.