I think you might have it backwards. I’ve always understood that hunting an animal for food is forbidden since an animal must be properly slaughtered and an animal killed in a hunt would not be kosher. Hunting animals to control population or for their hides or other parts is permissible.
That is one reason why venison (deer meat), a kosher animal because it chews its cud and has cloven hooves, can be eaten but is not because it is not a domesticated animal that can be properly slaughtered.
“I think you might have it backwards.”
No, you just misread what I wrote.