Show me any statistic, article, prophecy, or bathroom grafitti, which proves that is a true statement.
Check the numbers in France or UK or Sweden if you have to.
I think any demand lowered by killing earning potential, and I'll admit it's a semi-logical assumption if you think doctors are only in it for the money (I don't), could be offset by lowering the cost of medical school. Hence lowering the risk.
Doctors will still live really comfortable lives. They will just live in mansions, rather then on estates. Their daughters will get a mustang for their 16th, rather than a Porsch. It's a hard life, but it's probably worth the result.