In Europe there are labour issues that are somewhat similar. Eastern European job agencies are sending people to work here Western Europe as labourers construction workers or truckers, at far lower wages. The issue is not one of immigration, but what amounts to circumventing minimum wage laws and such. A proposed solution is to require "like pay for like work in the same location": foreign companies sending their employees here on a long-term job (essentially indeterminate) would be required to pay them locally prevailing wages. This would make it even more attractive for foreign talent to come work here, but it would also mean that cost would no longer be a reason to hire foreigners, but filling positions with scarce foreign talent would still be viable. Perhaps that would also be a reasonable fix for the US H1B programme? IIRC, Trump already suggested to increase the minimum wage for H1B workers.