Specifically, labor shortages lead to higher salaries for those groups who no longer have to compete with the type of immigrants that used to come, and only if

Specifically, labor shortages lead to higher salaries for those groups who no longer have to compete with the type of immigrants that used to come, and only if the demand is limited. But for most other groups, it may lead to a reduction in real salaries, due to price inflation. Fewer carpenters makes housing more expensive, and fewer tech workers can make many businesses (especially those outside core tech that still depend on such workers) more expensive to run. And for workers in global hubs, one could argue that the concentration in one geographic location (including immigration) has actually lead to higher demand due to the increase in vibrancy and rate of innovation, leading to an increase in salaries.