We tried that (no reevaluation though). The problem is, could doctors then be responsible when someone they evaluated capable of having gun commits a crime?
Because our law (changed after two school shootings a decade ago) didn't specifically say "no", doctors' union refused from making any such evaluations, leading to months that nobody who didn't already have guns could get a new licence.
Actually, I'm not quite sure how that was resolved in the end.
But on the other hand if the doctors have no responsibility and they get paid for evaluations, people will go to the doctor who OKs everyone.
It's not a bad idea, but the problem is how to execute it in practice.