If you think you cant shoot the deer population out you are wrong. Why did we have to restock the countryside with deer the first time?
Deer were nearly eradicated by market hunting, where there were no rules what-so-ever. Night hunting, jack-lighting, no seasons, no limits, almost no forest for deer to hide in (nearly the entire Eastern U.S. was deforested near the turn of the 20th Century, when deer were nearly eradicated), venison legal for sale, etc.
Deer weren't nearly eradicated by sport hunters, they were eradicated by market hunters killing and selling deer to the eastern meat markets by the tens of thousands.