Lots of Americans are descendants of seafarers of different nationalities that jumped ship and eventually became good American citizens. Probably some on this forum can trace their ancestry to such persons.
Today it is harder to do so, with inward and outward clearance being a lot stricter. If a person arriving on a ship as crew is not present when that ship depart, surely the Master will have to explain why and document the reason.
Other countries are also attractive places for people from 3rd world countries to jump ship and just disappear if it was easy to do so. But they are not restricting shore leave for seafarers. Why???
I remember back in the old days (1960’s-70’s), when there were still a large number of American seafarers around, that some of them got left behind in ports in Asia. (Other nationalities too)
Japan had special prison for foreigners (in Kawasaki, as far as I remember) where they were kept until the ship were leaving Japan, or they were sent home as Supernumerary on some other ship.
Are you going to stop tourist and business visitors as well? Some of them may overstay their visa.
What about foreign students, many of whom do not want to leave at the end of their studies?
USA has a reputation for drugs, violence and gun culture. Maybe other countries should restrict shore leave for American seafarers, just in case they could possibly want to bring their dangerous culture to foreign shores?