Deer behave differently in the presence of predators. They migrate less, the reproduce more manageably. Overpopulation of deer results in overgrazing where they can effectively kill entire species of plants or desertify areas. We’ve engineered an environment without their natural predators.
Culling and hunting them is different than if we caught and release neutered them.
I’m not a hunter, and I’d be fine if we just introduced wild predators like wolves (I saw a study that this was actually healthy to their population).