For Sure!I don't see the harm in keeping numbers down with varmints, yes they will eventually show up again, but if you don't keep numbers down, that one coon, will turn into 20, etc.. Been there done that on the farm growing up, we got 20 in one evenings sitting.
Since we've displaced their habitat (and more importantly their natural predators habitat) and fed them to overpopulation with our garbage (intentionally or not)...IMO, it is our duty to become the 'apex predator' and kill them when they become a problem to the extent that we need to trap them.