In Germany, many people indeed say if you are not deeply into the topic that you study, you should rather get a vocational training (Ausbildung), or attend a different kind of tertiary education than a university such as
- Fachhochschule
- Berufsakademie
(these words have no good English translation). Basically these are kinds of tertiary education that are more applied than the much more scientific training that you get at a university.
Specifically for mathematics (I guess the same holds for physics), a lot of people say that if you don't consider it to be an ideal life to think about math exercise sheets when you sit in the bathtub while other people are having fun at some party, you simply are not made for studying mathematics and should change your degree course as soon as possible.
We haven't regained traditional apprenticeship roles (perhaps because we so weakened unions?) but 30 (of 50) States have free or heavily subsidized two-year community / vocational college programs. Affordable and accessible vocational education opportunities are increasingly present. I also think (very subjectively) that we are seeing a renewed respect for the trades.
However, there are structural headwinds outside of education - no national health insurance plan being a major one. Farming, fishing, forestry, construction and similar trades still have a 20-30% uninsured rate in the US. (The uninsured rate in white collar "professional" work is around 2.5%.)
The reason for the traditional apprenticeship roles is not unions, but rather capitalistic:
- If potential employees are well-trained the employer doesn't have to invest resources for training them.
- The certificate of the vocational training means that the employer knows that an applicant has an established standard, and can save time testing whether he is qualified.
- Because the trainee needs practical experience, employers can invoice this additional worker to the customer. Because the trainee needs explanations and thus works slower, more hours can be invoiced to a customer.