I think there are lots of parts to this puzzle. I work properties that were once awesome turkey and deer hunting properties. Each of these properties have the same thing in common. They are covered with raccoons, coyotes, and hogs. I wish there were more studies to evaluate these impacts. I believe these 3 do have an impact on the populations and I have had that belief well before I started a business.
Hunting clubs need to start addressing all of these issues just like they do food plots and prescribed burnings.
A combination of dropping the limit and addressing the predators could help turkeys rebound in just a few years. Deer will take much longer.