I think we need to be careful what we wish for.
Tennessee already has one of the longest turkey seasons in the U.S. with a 4-bird limit. We're already free to exclusively bow hunt every day of it, if we wish.
Establishing new special weapons seasons (unnecessarily) could cause more division and rift among hunters than it creates in real added hunting opportunity, i.e. most hunters do not even own any archery tackle.
What I'm saying is that we may do better thinking more about just hunting, than with which particular weapons hunting is allowed.