It seems to me that IF it has been clearly established that the traditional/earlier season starting dates have no impact on breeding/fertility, then any decision to return to those traditional dates might best be determined by polling the state's turkey hunters to see what they prefer?...
Having said that, it is counterintuitive to me to think that starting to hunt BEFORE turkeys have had a chance to breed for a period of time prior to hunting them is a good idea...especially in struggling turkey populations. So, the question that comes to my mind is "when do the turkeys in a state actually begin to breed?" Having a firm grasp on that might make establishing season dates based a bit more on science rather than "guess and by gosh" like it seems some states do.
My conclusion, or speculation, in this specific instance is that the TN turkeys in question are/were perhaps initiating breeding a week or two before the traditional early starting dates...which would indicate to me that there is some degree of breeding saturation occurring prior to hunting them. In my mind, that would account for the study's findings.
Regardless, as a general statement, I am personally a proponent of a management strategy that includes not starting to hunt before the turkeys have had a reasonable opportunity to breed. I just fundamentally think that is a good idea.