Would be fine with me if we could totally eradicate coyotes in Tennessee, but that appears to be impossible.
Are coyotes a native species to Tennessee?
I'd be totally fine with us humans sharing the apex predator role here with only foxes and bobcats in Middle & West TN. If we didn't have so many coyotes, I believe we would have a much larger fox population. (And the black bears can stay in East TN where they can better co-exist with humans.)
In the meantime, in most parts of TN, I believe the coyote population is more up or down based more on rabbit and other "small" meal populations, and are not generally as much a threat to deer as is generally thought. However, I do believe certain individual coyotes do focus on deer more than others, and I have witnessed large male coyotes seeming to do this, even on adult deer. But most of the time, it is the smell of blood that causes coyotes to specifically go for a particular deer. I have no doubt that many deer that get wounded (either from a hunter's poor shooting or fighting with another deer) are specifically "dogged" by coyotes and killed by them, when they would have otherwise recovered from their wounds in the absence of coyotes. This just adds to the importance of our only taking very high probability shots, as even a small "nick" anywhere on that deer is likely to cause that deer to be "dogged" and killed by coyotes.
Back to Dr. Woods, many may not realize what an accomplished deer hunter he is.
And relating the deer hunting to coyotes, if I remember correctly, he once said something to the effect that deer were much easier to hunt in places where coyotes do not exist. The implication was that deer that lived along side coyotes were always much more alert and wary than deer than were not constantly on the alert for these predators.