Because the non-spayed deer will just procreate more. You’re not doing population control at all with your approach, even if it was possible. I ask you, do you think you can take a fishing pole and fish a lake empty? No, ofc not, that is ridiculous. What your proposing is equally if not more ridiculous. You’re thinking about nature as if it was a fenced area that you are in charge of. Very arrogant of you, tbh.
You’re the type of person who gives veganism a bad name, imo. You’re probably one of those people who think “Thanos was right”, huh?