This is really a weird requirement and most other places in the world don't have it, without suffering any setbacks when it comes to outcomes of treatments.

Imagine that every programmer would have to study, say, Latin for 4 years before being allowed to code.

Agreed. It might make some sense to require undergrad chemistry and biology for med school applicants but presumably that could be squeezed into 2 years of undergrad. Possibly a customized curriculum could teach it faster or as part of med school.

Mine was in political science.

In Canada there are some universities which allow exceptional students to apply after the first 2 years.