Either you haven't thought this all way through or you are intentionally ignoring the whole host of other emotional and logical arguments around gun control.

If we're talking about gun control, fine. I'm all for reasonable gun control. I don't think targeting hunting rifles/shotguns are the most useful though. Handguns are the issue there. Still, yeah, more good gun control would be nice. Not really part of this discussion though, but that's the one argument I did consider, but doesn't really apply to hunting weapons. If we can get it passed for the weapons that actually matter, then I'd agree losing hunting weapons are fine.

That's only true in an ecosystem where the predator (us) and the prey are in natural equilibrium, which I’m sure you'll agree is absolutely not the case.

Without that natural equilibrium you need formal and enforced regulation to make this work.

Yes. That formal enforced regulation needs to exist, and I don't know anywhere that it doesn't. In the US, you need a license, and you can only kill a certain number of the animal per season, and that's all based on how many of the animals need to be culled, and it does need to be done. Equilibrium is maintained through this regulation.

This magical "naturally healthy" state of existence glosses over a lot of problems with that statement.

I never said "naturally healthy". I said they evolved to have a certain percentage of losses. If that isn't maintained by other predators, we need to do it. It's naturally (in its current state) unhealthy. Hunting is required to keep it healthy.

we are also animals, so us dying and being eaten also fall under this, so by that rationale another effective solution could be to reintroduce more (non-human) predators and a few of us die here and there, but the animal populations now stay under control.

Sure. That'd be another solution. If we're discussing policy, I think we can safely ignore it though. There's a lot of solutions that are not going to happen. We don't need to rule out all of them to discuss what we actually can do.

Until a new equilibrium is reached, because that's how ecosystems work (or collapse, depending).

No. They boom and collapse. This repeats, until evolution takes it's course maybe, which will be quite a while. It doesn't reach an equilibrium state because they evolutionary pressures were different when they evolved. Maybe this isn't true for all prey animals, but many, such as deer and rabbits, it is. Population booms, they eat all easily available food, they die off from starvation or disease, then they boom back.

A lot of your argument against hunting is that it requires regulation. No one is arguing against that. It is needed, and this is already recognized and enforced. We just need to now enforce participation in a way that doesn't create negative externalities from lead poisoning.