When I was younger my friends and I used to trap and kill dozens of them at a time. The sheer number of hogs and the rate at which they breed down in the river bottoms is insane.
Not sure how you'd ever get rid of them, they are pretty clever and once you use a trick unsuccessfully on them they tend to avoid it.
Biological warfare, in one form or another, might be the only way, but that comes with risks that are probably unacceptable, even in light of the amount of damage they cause.
But you don't shoot one. You shoot most of them. That requires thermal optics, semi-automatic rifles, high capacity magazines (and lots of them), ATVs or helicopters or well-planned stands with a good view of a clearing that hogs might hang out in at night.
Not sure how you'd ever get rid of them, they are pretty clever and once you use a trick unsuccessfully on them they tend to avoid it.