I read all the turkey research that I can and I've read a lot over the years. The Turkeys for Tomorrow organization also has some excellent videos on YouTube with biologists discussing the latest research - I would summarize it by saying that any population decline in turkeys is primarily due to an increase in predators. Many places have more nest predators than ever, and there's also a big increase in many avian predators, and the big problem with them is that they are protected by federal law.
I haven't read anything that documented coyotes as a net positive. If that research is available I'd certainly like to read it if anyone has a link. I have read that coyotes are the biggest predators of fawns and they get a high % of them in some places that don't have a lot of ground cover.
Anecdotal evidence I have is that I have called up 7 or 8 coyotes over the years while turkey hunting, including one last week. I don't think they would waste their energy coming to a turkey call unless they had some hope of a turkey dinner. I've never seen a coyote catch a turkey, but a friend of mine saw one catch a hen a while back, and she managed to escape leaving a leg behind.
All this to say that predator control is an important part of turkey management, and I will continue to include coyotes in that group absent research proving they are a net positive. All that I have read says bobcats are worse. One study had gps on 4 adult gobblers and bobcats got all 4 of them. Great horned owls are also capable of taking mature gobblers, but they are protected by law.