I don't buy the comments regarding litter of 12... What a joke.... Perhaps in the south, with mild weather, but not here in MI. Thats equivalent to saying that when the baby daddy walks out on the momma, that she is going to add a bunch more offspring, raise them herself and increase her standard of living.....
Every coyote I have killed has meant less food getting back to the den and potentially pups without a mother. In winter, most of the time pups without a mother will not survive. Mating is in Febuary and pups are born in ~April and weaned by May. They still take another 11 months to reach maturity so are particularly vulnerable the first winter. Given the fact that Michigan has now had 3 exceptionally mild winters in succession, it is a definite factor in allowing larger numbers of coyotes to survive. Human activity, in the form of road kill, is a substantial factor in their survival in winter. If road kill got cleaned up they would be denied this easy resource. The wounded deer that hunters abandon is yet another source and I think that is a subject few want to discuss.
If you are trying to run a business with livestock, it is an uphill battle. DNR designating the coyote as a game species is simply a matter of control (over hunters) and source of revenue. There are exceptions in the law for anyone farming and experiencing damage, but most of the time, the farmer does not have time to attend to the predators personally since most have a second job to stay solvent along with the common lack of labor on smaller farming operations. Coyotes being as prolific as they are, it still takes a LOT of time investment as well as plenty of specialized equipment to have anything more than a token effect on the population. The "professionals" chase them down with dogs and have a large team of shooters, but it is pretty expensive.
Its mainly city folk who are champions for the wolf and coyote, or hobby farmers who do not rely on income from their operation. Securing pastures against coyotes in an effective manner can be done, but is again expensive and high maintenance. I have met alpaca breeders who had 8 ft high "no climb" fences around their pastures along with electrified cattle fence on the outside to deter cattle and bears, but the cost to wrap 100 acres with that kind of material would be eye watering for sure... Most ranchers I met were barely scraping by financially, but were in it for the "lifestyle" and the quality of life.