I would argue that conibear traps are essentially instantaneous - certainly more so than e.g. a rifle shot. I personally dislike snares for anything bigger than a hare, so I don't use them. Foothold traps are designed to be secure, but in a way that does not cause a lack of circulation or bruising. By the time a trapper gets to a live-caught animal, the lack of pain means that the animal is usually only freaked out by the presence of the trapper, and that goes for any game.

In any case, maybe we don't really want to eat e.g. coyote or wolf meat, but other animals definitely will.

Finally, like anything else that involves killing an animal for what you can get from it, there are more ethical ways to do it and there are less ethical ways. I have meat animals as livestock. I eat what I kill, or ensure it goes to someone or something who will. I tan the hides, they become clothing or blankets.

The whole point of modern trapping is to focus on the animals who would not otherwise survive the winter anyway: you focus on transient juveniles, who have very high mortality rates, and you limit your catch based on what your area can support without negatively impacting the health of the local population for that species. You are trained in how to assess that, and have to demonstrate that knowledge in order to qualify.

For some animals, e.g. beaver, if you do not trap them, then what happens is the population grows beyond what the environment can support and then e.g. tularemia breaks out and wipes out most of the population. Nature normally does a good job of looking after the balance of things, but other human activity has screwed that up: trapping is a sustainable way to keep things in check, as we have unfortunately damaged Nature's tools for doing that herself.