A lot of those trades are getting covered up with illegals, in many parts of the country.
You're probably right, though, about skilled trades with high barriers to entry, like plumbing and electrical.
True for a few trades but serious housing construction work requires an apprenticeship program, and that usually cuts out the majority of the illegals right there. When I do my morning walks every day I go by a house that is being completely reconstructed I see a bunch of Mexican-Americans doing the work--all speaking good English and driving recent-production Ford, Chevrolet, GMC and Dodge trucks to the work site. I asked how much they're making and a few told me about US$40 per hour.