I think Filipinos, Mexicans, and many other nationalities would leap at the chance for U.S. citizenship in exchange for service in the military or a foreign legion. The Philippines and India should be two of our main recruiting targets, as many of the locals speak English already.
We need to examine the root problem, we have the largest population (by far) we have ever had, we have the smallest military in generations, yet we are absolutely desperate for warm bodies.
The army and marines want to increase their numbers, the army alone wants about 9 additional brigades. We need to find out why our young men (even active duty airmen and sailors losing their jobs) will not serve in our army and marines.
Something is broke in America and we need to decide what it is and fix it. Replacing American GIs with permanent foreign divisions is a mistake.