Just because something happens on its own in nature doesn’t mean it’s a good thing per se - for instance, I prefer the warmth of my heated house over the "natural" cold temperatures of the winter months. That’s the famous "appeal to nature" fallacy right there.

Also, like others already pointed out, hunting deer is only necessary because we eradicated most of their natural predators. Making the case for hunting today in order to fix a problem hunting created in the past feels oddly circular to me.