The Richmond Fed has a good overview of apprenticeships in the United States and some of the academic literature:
According to a 2013 World Bank and International Labour Office study, only about 0.3 percent of the total U.S. workforce is in registered apprenticeships — about a 12th of the share in Germany. But some states, including South Carolina, have expanded “dual system” apprenticeships in recent years by building partnerships between colleges and firms and, in some cases, offering tax credits. Through the state’s “Apprenticeship Carolina” program, about 27,000 workers have been trained since 2007, including many at foreign-owned firms. Nationwide, there were about 505,000 registered apprentices in 2016, according to the U.S. Labor Department.
The review offers some useful ideas on why apprenticeships are less common in the United States. One problem is cultural:
In other countries, it’s more likely that college is seen as one option among many, and apprenticeships are considered a worthwhile route to middle-class employment. In the United States, parents are more likely to see college as a vital investment without considering other alternatives…
As I said in Launching the Innovation Renaissance:
The U.S. has paved a single road to knowledge, the road through the classroom. “Sit down, stay quiet, and absorb. Do this for 12 to 16 years,” we tell the students, “and all will be well.” Most of them, however, crash before they reach the end of the road — some drop out of high school and then more drop out of college. Who can blame them? Sit-down learning is not for everyone, perhaps not even for most people. There are many roads to knowledge.