Medical school admissions vs. STEM PhD admissions in the United States
This may have changed but we studied cartels in college and the American Medical Association (AMA) was called a cartel by my professor.

In the US the AMA not only sanctions the medical schools but puts a count on how many students can be accepted. Since there are a limited number of slots competition is more fierce.  

There is no external body limiting STEM or other graduate school departments.

STEM and other PhD can get grants as they are producing a product (thesis) that can be (and often is) sponsored.  

In medical school the only product is medical training for the student. There is little to no incentive to sponsor a medical degree.