Where did I endorse "a priori restraint" on RKBA? Just because I recognize that common sense precludes an absolutely unrestricted RKBA, does not mean that I approve of background checks, registration schemes, purchases-per-month limits, or anything else that restricts the rights of law-abiding citizens. Someone who shouts "Fire!" in a crowded theater is punished AFTER doing so; no one has suggested gagging all theater-goers before they enter the theater, in order to prevent such dangerous exclamations. However, if we take preposterous positions, such as holding that a diagnosed paranoid schizophrenic cannot be prohibited from legally possessing a gun, we'll lose this very important battle.
The Constitution states "shall not be infringed". Ie; no restrictions. Removal of Rights as punishment requires conviction, ie; due process.
He can, but only through an individual due process. You can't pass a blanket ban on all "diagnosed paranoid schizophrenics" possessing firearms, UNLESS that law provides for an individual finding, in a court if the individual requests, that the person is prohibited from owning firearms.
However, "common sense" notwithstanding, such a law will prevent very few "paranoid schizophrenics" from obtaining and misusing weapons, any more than current laws prevent convicted felons from obtaining them.