Re: 'Murica never ceases...
What happens on private land? So assuming a large enough chunk of land to support a deer herd, would culling be a matter for the land owner, or would that still be permitted/regulated? I'm assuming a sensible landowner who understands why there are closed & open seasons.
Laws for private landowners typically are regulated by whatever jurisdiction they are in although there may be additional restrictions or allowances compared to hunting on public lands. Also, it should be noted that hunting wild animals is different in many locales than hunting in a game park for animals raised for the purpose. I am unfamiliar with which laws apply in those cases as I have never dealt with them, but I am aware they are not necessarily the same as for hunting wild animals. I know that in some areas, landowners are allowed extra permits specifically to be used on their property in addition to any used on public lands. Also, where friction often occurs is between farmers who are not pleased with wild animals raiding their crops and the state which claims the ability to dictate who can dispose of which animals.
I should note for those who are unfamiliar with animal populations in the US in general, and especially deer, we have plenty of wildlife that encroaches into urban areas. I work in the Washington DC area and have found deer in my front yard (I live in a townhouse community) and have even seen them along the beltway which is well within a very built-up urban area. As noted elsewhere, the lack of animal predators have allowed some species to flourish. That is not to say that there have not been efforts to bring back those predators. For example, there has been a successful* program to re-establish the black bear in Louisiana.
* The definition of "successful" depending on how you feel about a large omnivore living in proximity to humans.