Tim Fernholz has a great post about immigration and the evolution of the manicure industry in California based on a study (PDF) showing that the influx of Vietnamese immigrants into the industry overwhelmingly led to more manicures rather than displacement of existing manicurists.
It's an excellent illustration of the point that even less-skilled workers raise average living standards, and also of how basically goofy the idea of trying to decide whether or there's objectively a "labor shortage" in some field. There is not some fixed stock of manicures that society strictly needs. What happens when you increase the supply of workers is that you change the shape of the marketplace. As Fernholz writes:
Why was this possible? Because the immigrants were—wait for it—innovators in the manicure space. They developed the idea of the standalone nail salon that reduced costs, “making a once-exclusive service commonplace.” That meant more nails to paint, not just more workers per nail. The benefits of immigration accrued to people who got their nails painted, to the new immigrants, and even to the remaining non-Vietnamese manicurists.
This is the stuff of what improved living standards are made. That said, the logic that applies to relatively low-skilled service work like manicures also applies to higher-skilled work. It's unfortunate that for a range of political reasons the entire discourse around skilled migrants has ended up rather narrowly focused on engineers working in the high-tech industry. As Dean Baker's been writing for a while now, we need to think of the portability of human beings and their professional licenses as a tool for free trade in things like medical and legal services.