There's also the issue that--as I understand it (it's been poorly articulated/operationalized)--you're basically being asked to predict behavior over an extremely long period of future time (e.g., for the duration of this person's owning of the firearm...possibly the rest of his/her life) vs. making a prediction over a more modest (1 week) time frame. I think this area is a bloody mess, frankly, and the only thing we can really be expected to do is assess imminent risk of violence (such as we already do in the context of determining if someone meets criteria for involuntary hospitalization at a particular point in time due to, for example, specific threats of serious violence, especially against named/specific individuals. The question of, 'Is this person okay to possess/carry a firearm? Are they gonna be the next mass shooter (or will they shoot their spouse) at some point over the next 20 years?' isn't really something that we've mapped out yet as a profession. I think the legislation and public outcry for 'mental health assessment' to predict/prevent these sorts of extremely rare events is way out ahead of any tractable psychological technology to actually do so reliably and validly. We don't have a crystal ball.
So, I agree with you on the very poor positive predictive value of many of these assessments.
However, you have it backwards in terms of ability to predict outcomes. In fact, ability to predict an outcome INCREASES the longer time period you look out because of the increasing prevalence of the event over time. This is very relevant in suicide risk evaluations. So actually, I'm much more comfortable saying someone has a CHRONICALLY elevated risk of suicide compared to the general population statistically due to risk factors because that's what's actually been studied. If you look at outcome assessments for suicide for instance, no studies generally look at risk factors relative to outcome for a time period <6 months and most of them look at years of followup.
We absolutely should NOT assert ourselves as being able in any way, shape or form to predict SHORT TERM risk because, statistically, we are terrible at this. Literally it seems no better than chance, you'd have just as much predictive value flipping a coin and discharging people from the ER. Again, this makes sense because of the relative rarity of these events (suicide, mass murders, etc). Do we still attempt to do this? Yes. Is it primarily a legal CYA thing? Absolutely.
So, it makes much more sense from an actual data standpoint to say "I believe this person is at an elevated long term risk of suicide due to their prior suicide attempt, major depressive disorder diagnosis, lack of social support, ongoing poorly controlled substance use. Because of this, I recommend they engage in long term longitudinal psychotherapy, substance use disorder treatment and psychiatric medication management to attempt to decrease this risk over time."
It also makes more sense to say "I believe this person is an elevated long term risk of homicide/threat to others due to their diagnosis of antisocial personality disorder, history of multiple violent offenses, poor impulse control, substance use, etc" rather than "I think this person is an acute risk of killing someone next week because of X risk factors". There is much more data for the former than the latter.