They actually don’t. I’ve raised pigs, and they keep themselves clean- they pick one corner of the pen to shit in and a different corner to sleep and eat in, given the opportunity. The idea that they shit where they eat is probably (dunno for sure) because they clean themselves by taking dust baths, and when it rains, the wallow turns into mud. They roll in the mud to stay cool when it’s hot sometimes, but it isn’t shit.

We had a pig when I was a kid who could work the lock on her pen and escape into the fields next door to eat grass. They’re pretty smart.