Solving essential medical services like the ER is surprisingly simple

Abolish the undergraduate medical system. Specialize the majors.
Abolish the general practitioner license after medical school graduation.
Subdivide medical licenses so that students must follow the intern-to-resident sequence.
And by subdividing medical licenses based on their undergraduate major,
make it so that licenses are issued only for those specific fields.
Instead of a single license, split it into dozens of specialized licenses,
require exams for each, and prohibit general practice.
If you do that, they won't be able to avoid essential medical services.