Actually they aren't handled at all in western and southern Europe because those regions have never had as many feral pigs as exist in the Americas. Also it has nothing to do with predators and more to do with the ecosystem that the animal is in.

Seriously, go do some actual research on the impact of invasive non-native plants and animals on the ecosystems they're introduced to.

Wild pigs in Europe are known to breed less than the hogs in the Americas as the pigs in European woods are all mostly Eurasian boar whereas hogs in the Americas are mostly descended from escaped or intentionally released domesticated swine which were selectively bred to have larger litters, hence why they're called feral hogs. Add that to the larger variety of plants that the hogs can easily feed on