I’m not studied on this but I think you hit on the most major parts - the capitalists want immigrants for cheap domestic labor, and benefit from those immigrants being in a precarious socioeconomic position. At the same time, they want to maintain the divide between the imperial core and the global south, which requires that capital be far more mobile than the working populations are allowed to be. If you allow too few immigrants in, then there’s a labor shortage and worse domestic investment prospects; If you allow too many immigrants in, it becomes harder to maintain the heightened rate of exploitation that they are subjected to, both here and elsewhere.

Immigrants are turned away and deported to manage this balance, and as part of the superstructure- the turning away of immigrants is a necessary part of maintaining the myth of American exceptionalism, which in turn keeps the empire running and keeps workers worried about the ‘national interest' that just so happens to always align with business interests