This is a great question, and is a big talking point of hunters I have heard. I certainly am no expert on this, and it is difficult to find any analysis of the claim. The claim often goes something like, "Deer no longer have natural predators, and if human hunters did not go after them, they would ruin the ecosystem and overrun the farms and suburbs."

Yet, I find this kind of hard to believe, because hunting is not really an altruistic activity. It involves paying a license fee and is essentially a hobby people enjoy doing, not a donation of volunteer time for the good of the ecosystem. Also, because of the license fees, various "natural resources" state agencies encourage deer to propagate so hunters have enough prey. This involves techniques like clear cutting sections of forest so deer have more edible vegetation (the area where field meets forest is good for that). So in a way, isn't this actually contributing to the "overrun" problem?

Other techniques can help resolve the situation of an imbalanced ecosystem. 1) Re-wild larger sections of land and introduce small bands of GPS-tagged predators (wolves as was done in some areas of Canada). This would require pushing back against urban sprawl and animal farming. 2) Commission conservation agencies to shoot deer with birth control from rifles. Repeat as necessary. 3) Let the deer run out of food so they naturally have less surviving to reproducing age. It's not just predators that control population.