The Economic Policy Institute published an interesting piece of research on the links between H1B visas and lower wages paid by the U.S. employers for key skills: https://www.epi.org/publication/h-1b-visas-and-prevailing-wage-levels/. As far as I can see, the report does not cover academic faculty employment, but it does cover data from universities and other non-profits.
The report is worth reading.
