Honestly, culling is besides the point I am making, since the primary goal of culling is not meat production.
There are morally more ambiguous cases (than with slaughter for meat) in which killing an animal can be arguably better than to let it live. Putting down a terminally sick pet is an example. Culling might also be argued, but I would not say that it is "not cruel or even morally ambiguous".
With culling, my thoughts on it are these. When we refer to culling, we most often talk about culling in farm animal situation. As in, there is a sick animal that has to be culled so that the population doesn't become infected. Or we kill the male chicks because we cannot raise them to become egg producing hens and keeping a lot of roosters together can cause problems. The killing of farm cows that underproduce is also a form of culling. I would argue that none of these killings would be necessary in the first place if we didn't have big scale farming (or, for that matter, farming of any kind) of lifestock. My guess is that with
Modern farming is very much none of those things though.
we agree here.
Culling of wild animals is more controversial. As far as I am aware of, hunters are being told how many animals of a certain species and sex they can kill in a hunting season and it is regardes as population control. (Whilst we ofter created conditions in which the population cannot control itself.) Or they get an order from a farmer etc. to kill a chicken ripping wolf. If you have to kill a wolf because it regularly attacks your chicken farm, then the chicken farm is the actual problem, not the wolf. Apart from that, you'll end up fucking with natural selection. Arguably not very great. But since we can't just go back to the caves and restore nature the way it was before civilization and so on, some form of culling of wild animals will probably stay necessary for human survival and artifical balance of and artificialized nature - even without farming of lifestock. I would not call this ethical or morally right, but a realistic, awful necessity.
I'm not sure about the point you're making with native americans. When I search for native american hunting practices the first thing that pops up is how they hunted bisons and nearly drove them to extinction, which is also the most prominent example I know of. This goes into the territory of the idea of the Noble Native. But I doubt you meant that as an example.