Can you show me one example where hunting has successfully kept a nascent wild population in check? I'm not agreeing with you on your first point until you can prove its true and applicable to the current situation in Canada.
From what I can see, the moment you open hunting you get bad actors who will want the pig hunt to last in perpetuity and will do things to maximize the chances of that, regardless of the law. Also, If you legalize hog hunting people will become economically tied to it through guiding, equipment, or other industries. It doesn't matter what you regulate, there will be people who don't follow those rules, especially because a lot of things you might want to do like put in rules about "you must attempt to kill all pigs in a group", or "you must target females first" is impossible to enforce in the field.
The potential harm caused by opening hunting is massive, and you have to consider the human element. And I'm not sure if you've noticed, but a lot of people suck.