Setting aside the fact that I'd be witness to less deaths because I've chosen a more effective protocol for population control, I think letting them live out their lives isn't a net negative. Why would I expend energy ending lives if they don't impact mine?
Granted, there are times when euthanasia would be necessary. For example, feral dog populations in areas where the vulture population has died off, where they carry disease and attack passersby and the supply of food is basically uncontrollable, I get it. But that's a case I personally would preemptively qualify if I were considering it.
