What they are already doing with background checks is already some modicum level of safety. What you are suggesting is throwing the doctor/patient confidentiality out the window and letting the government pretty much have free run at anything. It's already bad enough that the Patriot act throws many things out the window already like the Wiretap Act. Hell, Boston already showed that you can be killed if you think about killing a police officer (see Minority Report). How about the war on drugs, and taking kingpins and their cash down. Then the police expanding that so that they can take any cash from anyone for just the inference that it might have something to do with drugs, then making you prove that it wasn't. All the while they don't have to charge you with any crime, they just keep whatever loot they want. How about the war on drugs then expanded to impound rights for DUI's, even if you were found not to be DUI.
So no. In no way should the government get a foothold on using psych tests to screen people.