The truly psychotic, whose first act of outward violence is murder or mass murder are quite rare, and thus not statistically significant enough to risk the rights of everyone else.
Take the truly "broken"...like the infamous serial killers, plus all the mass murderers, and you end up with a very small number of overall homicides. Thus, mental health screening for firearms is a terrifyingly slippery slope for everyone else, and doesn't have a statistical effect--it ends up being an "if it saves just one life" fallacious argument that costs everyone else.
Psychology isn't predictive enough to do this, and even if it did, laws that punish the POTENTIAL to do things are bordering on Orwellian thought crime, not to mention in flagrant violation of multiple constitutional aspects.