Because it’s illegal, it is often done without any respect for the site, sometimes with heavy equipment like backhoes. The potential high value of old pottery leads people to dig up sites, destroying their usefulness for serious archaeological study as well as disturbing human remains.
The closest analog here in the southwestern US is pot hunting in Anasazi (and Pueblo, and other cultures) ruins, and that is an activity very much frowned upon. I’ve been watching some videos on YouTube of this sort of thing, and I’m curious what you guys think of it. I expect this is a subject more familiar to our European readers than folks here in the US – the idea is tromping out to the sites of WWII skirmishes or battles with a shovel and a metal detector, and digging up artifacts like helmets, canteens, firearms, ammo and casings, and other detritus of warfare.