> But the majority of undocumented migrants are visa overstayers. They get a legal visa to come to the US, often a visit visa, a student visa or a temporary work permit (eg J1, H2A, H2b) and just don't leave.

Yes, and that's a big part of the motivation for this policy of forcing people on temporary visas to physically leave the US in order to apply for permanent residency. It prevents people who get a temporary visa and plan to overstay that visa and nonetheless apply for some kind of pathway to permanent residency in the US from being able to do that.