Anything can be done incorrectly, but hunting is indeed a management tool, according to publicity from every Fish/Wildlife agency of which I've read--and that's a lot of reading, over more than forty years of it.
For instance, the numbers of a deer herd would increase exponentially, in the absence of predation and limits on food. A healthy doe always has twin fawns, and the female fawn can be impregnated at age 1-1/2. There is a fertile period of some five years--so the math is left as an exercise for the student.
As the herd increases to the carrying population of the ecosystem, two things happen: First, the average size of the animals decreases; second, the resistance to winter kill is reduced. The Hill Country near Austin in Central Texas shows a prime example of this. 1963 was a drouth year. In Llano, Mason and Brady counties, the hunters' kill was 15,000 deer. Texas Parks & Wildlife biologists claimed the winter kill was 17,000. Yet, the area was still considered to be over-populated--and those are relatively small counties.
Because of the declining number of hunters in many areas, the bag limits have had to be increased. In Texas, it is becoming more common that, "Before you can shoot a buck, shoot a doe." And, you'll notice that in another thread here in the hunt forum, many have commented they are meat hunters, more interested in taking does.
I grant that the publicity goes to big bucks, but a large percentage of all hunters take does, considering the meat to be more tender.
While not always true, larger bucks are commonly taken late in the hunting season. That means they have already bred does, and passed on their genes to a next generation.
As a generality, where there is strong anti-hunting sentiment, large numbers of deer interact with cars and are commonly nuisances to residential flower beds. This is not the case where there is a more proper balance of populations and food supply, as numerous observations over the years have shown. Since there is a shortage of four-legged predators, we two-legged predators are all that's left to control the population.
Note that with one exception, no game animal in North America is in declining numbers. Certainly, none are endangered by hunting. The Bighorn Sheep is "blitzed" by both overgrazing (sage replaces their winter grass) and residential development in the winter range. (Hunters are spending vast amounts of money on bighorn restoration projects.) I note that some species of geese are in decline due to "subsistence" hunting in Alaska and western Canada.
This oughta get you started,
Art