From what I've heard the reason for the hatians flooding springfield is some factory wanting them for cheap labor, if we knew who the factory was maybe an email campaign or boycott could be useful.
Maybe a don't work with scummy factory campaign as opposed to a don't work with scummy magazines campaign
Hence my point. Even a completely lax and open border in a purely free market doesn't equate to hordes of people flooding in. You kill the subsidy system and the whole migration racket goes with it.