That a fair number of people still believe that it's more "natural", and thus better, for the bulk of the herd to starve to death rather than a percentage of the herd being hunted is one of the more curious animal rights positions.
It makes sense from the point of view of "stop messing with it for fuck's sake".
Probably doesn't make the situation better one way or the other of course, deer population explosions are largely caused by humans having removed most of the top predators, and being significant stressors for the rest (https://www.theatlantic.com/science/archive/2019/07/humans-p...). The systems could probably recover if left alone, but that would require isolation (and mayhaps reintroductions) so predators can recover and retake their role, which is unlikely to happen outside of essentially exclusion zones like Pripyat / Chernobyl. Unless they're really unpopular / hard to access, most natural parks might have too much human presence for apex land predators to really be comfortable.
Some people are deeply offended by the idea that we are an apex predator.
They very much are, many pets will way overfeed themselves if given the opportunity.
Though it might also be human-inflicted, I don't know if wild animals will do so if provided with effortless unlimited amounts of food.
I would expect so though, most evolutionary environments simply don't set up organisms for an unlimited glut of free energy-dense food, when there's a glut of resources it's usually followed by some sort of crash, so organisms stock up as fast as they can in order to out-compete their peers once resources crash. If the glut doesn't end (which is essentially what modern advanced economies arrived at), neither does the tendency to stock up, because there's probably never been an evolutionary context (sustained for a long enough period) where that was an issue and thus allowed some organisms to outlive others.