Shoot whatever your heart desires. From a management perspective it is better to shoot poults at least half of them die before spring and they are least equipped to survive a bad winter. There can be too many turkeys in a given area, here in central WI we had the highest turkey population ever seen going into winter. Winter featured deep snow requiring turkeys to feed on buds, seeds above the snow line and insect larvae in the bark of trees. The flocks were huge and when they came into an area they stripped all the feed within a few days. Come March I found what looked to be whole flocks of dead turkey remains. Mother nature thinned them out and my spring turkey sightings were down. This fall we have lots of poults, the hatch was good.
Also I have read that dense populations of turkeys are very susceptible to host of poultry diseases.
I am going to respectfully disagree that a gobbler is any harder to kill in the fall than in the spring. Using the right strategies I have found gobblers a bit easier to kill in the fall than hens protecting broods. The proof is in my icon; those 3 turkeys are fall gobblers. One sported 2 ten inch beards and the others had 11 inches of beard each.
Besides does anyone else ever find themselves wishing for slightly fewer hens in the spring when those toms get "henned-up"?
If you agree with me call it fact; if you disagree - call it my opinion.
After all - we are talking turkey.