Gadolhadorah, neutering animals is an issur de’oraisa, just like eating pork. That it’s painless is irrelevant, and so is that it serves the interests of both the animals and the human population.
Imposing harm on an animal for no purpose other than some sick psychic satisfaction to a person is not “obviously” assur a priori; that is precisely what the Torah comes to forbid with עזוב תעזוב. Without that pasuk it would not be assur.
That doesn’t mean we would do it; a normal person doesn’t *want* to do such things. Even permitted cruelty, such as pulling a feather from a live bird just because you couldn’t be bothered getting up and finding or buying one from a dead bird, is something no normal person would do. But it would be a personal preference, not a halacha.