Although we are unenthusiastic about bringing back the draft, we aren’t any more enthusiastic about our military actively recuriting foreigners to defend our country.
This is not based on some vague, moralistic patriotic urge. It is based on a knowledge of late Roman history, and specifically the disaster that the British leader Vortigern induced when he brought the Saxons over to defend a newly independent Britain. Although late Roman emperors, pretenders, power challengers and generals had brought the "barbarians" in many times to defend the Empire, eventually these people basically moved in and took over, dismembering the Empire in the process.
If a country isn’t–or can’t–be defended by its own, sooner or later it will cease to exist.