I don't know about the cause of the problem elsewhere, but so-called "sportsmen" relocating and releasing the hogs is absolutely the cause of the problem in Middle Georgia. I was born in 1948 on the farm I grew up on. I never saw a feral hog until the early 90s. When deer hunters from Atlanta started leasing large tracts, they decided that their lease would be more useful if there was something to hunt before and after deer season.
I fought a verbal war with hog-doggers on the Georgia Outdoor News Forum for a year or so. None of them would condemn the relocation of feral pigs. They just saw it as a way to gain new hunting grounds. I think at least one state refused to allow a hunting season for feral pigs because the G&F authorities decided the hunters would only make the problem worse.
The hog doggers have absolutely no respect for property rights. Landlines mean absolutely nothing to them. Their excuse is "my dog can't read those posted signs."

Apparently, many of them can't read the signs either.
Sportsmanship, fair chase, and humane methods should not be part of the conversation regarding the eradication of feral pigs any more than it is when trying to eradicate roaches or rats. They are vermin, pure and simple. We have discovered that the best way to handle them when we find them in a field is to shoot the sows down first. Then, the pigs don't know which way to run and can be shot while they are milling round the dead sows. Leave a sow standing and she will take off for the woods and the pigs will follow. If it isn't too close to a house, the buzzards and coyotes do a good cleanup job.