Ehhhh I ain't buying the fawn a day bit. Show me any study that states that. If that were to be the case, the population would not be anywhere near what it is.
I also live on a current 300 head cow/calf operation, though I am not involved with it, and we have coyotes. In the decade I have been here, not one calf has been lost to a coyote. I also have free range chickens and again, I have not lost one chicken to a coyote. I have lost them to possums, vehicles and roaming dogs.
You are right though, there is a fine balance in nautre. And she is far better at keeping the balance than humans are. She was doing a fine job until we came along and fixed it.