Psychiatrists and psychologists would have to clear people. Sounds great in theory, doesn't work in practice. They already do here to get your (Illinois) FOID card back if deemed danger to self or others.
I know a guy who had to spend $10k on a forensic psychologist after some resident shrink had him involuntarily admitted after he had an adverse reaction to shellfish, had to be sedated and intubated, woke up and went ape shit because he didn't know where he was. And they weren't going to restore his rights. Even when a psychiatrist said nothing is wrong with him. Shrinks HATE guns. Even if you get VERY lucky drawing a gun friendly shrink, the government will just run you around.