You make a joke but you've hit on something. I would argue that the American model is "fettered" migration (also apparent in gulf states and plenty of other countries), that is you allow illegal immigration but use it as a strait jacket to bind the migrants in. You force them to work below minimum wage in poor conditions that your citizens would never accept and then marginalize and vilify them when you need a scapegoat. I would say that is "fettered" migration and it doesn't work great either.
