There is a reason why only those from affluent/foreign backgrounds go into medicine. They're the only ones who can "afford" to not make money right out of college.
Also, you can have a STEM-based undergraduate education as your pre-med, even math and computer science can count if you take the right additional electives. The two aren't mutually exclusive. It's a good fallback if you bomb out of getting into med school (or decide 3 years into ugrad that you don't want to apply).
It's not 100%, but I'd say there is definitely a push toward graduate education in the "STEM worker shortage" conversation.
Interestingly, a RAND study found that the reason people with choice don't get PhDs in STEM fields is because they aren't competitive with the "professions", or even para-professions in health related areas.
https://www.rand.org/content/dam/rand/pubs/issue_papers/2005...
US ICE has a list of degrees that includes a number of health related degrees: https://www.ice.gov/sites/default/files/documents/Document/2...
People on this site frequently gripe about medical school and residency slots.