If you even see venison in a restaurant, it's likely been shipped over from New Zealand. That's because a century ago, when it was legal to sell game, people kind of overdid things. It's why we don't have passenger pigeons any more. Deer themselves were extinct in Indiana and other areas for decades, until they were reintroduced by the states.
Obviously, that's not the case now. As the above ODFW photo indicates, we've got so many deer now that we've got another issue on our hands: people run into them with their vehicles over a million times a year, leading some to call for legalizing the sale of game - at least, of deer - once again. There's also the issue of increased incidence of Lyme disease, which - again - is a zoonotic disease transmissible to humans.
Although rural populations of deer are pretty well controlled by predators and human hunters, there's growing recognition that the suburban/urban populations need more effective management. That's where the idea of specially licensed, trained commercial hunters comes into play.
Dr. Anthony DeNicola, the founder of White Buffalo, a non-profit that professionally culls and sterilizes deer, adds that hunters would also need to prove their shooting proficiency as they’d likely be hunting in suburban areas.
That, of course would raise a whole slew of new issues, as the idea of taking out suburban deer would throw the Bambi-lovers into fits of apoplexy. As well, the paradigm would need to be shifted: for over a century, the emphasis in hunting culture has been to cultivate a preference for shooting a big buck; a preference that was inculcated back when states were reintroducing the ungulates and trying to grow their populations. Today, females need to be taken as well, yet the preference has become fairly deeply ingrained. That may be difficult to change among long-time hunters, but the commercial ones will likely prove more amenable to the transition.