That statement is ridiculous. Hunting seasons are for hunting as a sport, for the taking of game for those that enjoy consuming it and for controlling game populations.
If your game populations are out of control, it's because the your game department isn't encouraging the hunting of game appropriately and neither is your community.
Bragging about your state's gun laws is specious, since gun rights are about self protection, not hunting. Start hunting and eating venison. Hang some deer hides on your fence line. Every doe you eat is one that doesn't breed. It looks like you're allow to bag five or six deer a year, so do it.
Hunting seasons separate agricultural activity from pursuit of game to protect farmers from the hunters, and the hunters from the farmers (and both from themselves if they play both roles).
The theory that limiting taking results in more game for later years is nonsense. These animals have to eat, and if there's nothing to eat, they don't reproduce. If resources are limited there will be plenty of animals starving to death in the winter. With the removal of the wolves and other predators from the picture, ethical men must cull the herd to match the resource levels else the remaining animals are harmed.