You're interfering with the natural balance of species when you hunt predators for no reason. I'm a bit skeptical about the 80% part, but even if bobcats do depend heavily on wild turkeys, if there aren't enough bobcats to keep their numbers down, the turkey population will get out of control, encouraging disease and starvation. I don't know that there are enough turkey hunters to then easily get the turkey numbers back to the sustainable level.
I don't hunt (you would not want to be in the same woods as me with a gun, no doubt), and I don't have a problem with hunting prey animals like turkey and ducks and deer, but killing predators just because they irritate you is a whole different thing.