There is no statistics to support the idea psychiatric patient is more dangerous than ordinary people. They are more likely to be crime victims than being offenders. Most of them are perfectly normal while take medicine.

It is immoral to take away their rights of self defense.

Furthermore, psychiatric evaluations are notoriously unreliable. Most mass shooters who got evaluations were determined safe.

If your idea goes through, the government would have power to take away guns for anyone going through divouce, lost jobs etc.