I mostly agree with you. If you were managing the deer population, or the bear population, the fish or any population that was not privately-owned, you’d want to find the point where ALL the costs were balanced against ALL the benefits. So, the emission of greenhouses gases might be part of it. But, only a small part. Mostly, we like bio-diversity. We view the entire world as a zoo in which we can enjoy not simply seeing various life forms in isolation, but in their habitats, and as parts of bio-systems. This is a little tricky as, for example, we don’t want bears roaming off their reservations onto nearby ranches and towns. But, there’s no big problem with deer roaming a bit. So, how many permits should you issue for hunting camels? Maybe a lot. Indeed, instead of charging people to hunt camel, maybe you should pay them. By adjusting the price, we should be able to maintain or even enhance bio-diversity in the world, which, as you point out, sometimes means culling some populations in order to preserve space for other populations.
In most natural ecosystems nature takes care of its own. As an example, when the mice and rats over-populate because of excess rain and the resulting vegetation the hawks and owls seem to come out of nowhere to take care of the problem. When the vegetation dries out and the birds miss a few meals, most of them die.
When species that don’t belong are introduced and they have few natural predators they can wreak havoc on an ecosystem. I would kill them all out except for maybe a few in a preserve paid for with private money. They don’t belong there, they couldn’t have gotten there on their own and only human intervention put them there.
So far when humans decide to aid Mother Nature by introducing plant and animal species to unnatural habitats with no controls, it has mostly turned out badly.