Absolutely agree with this suggestion in particular (though other policies are good too). I know the VA has a similar approach in which a veteran contacts them worried about succumbing to an urge to kill themself, and priority 1 is temporarily creating distance between the person at risk and their guns. I've never had to do that, but during one particularly bad time I mentioned I have guns, they asked if I want help securing them, and then sent me free gun locks plus created a plan with me on how to create that space if necessary.
I think part of why people aren't more proactive with this is believing they might completely lose their guns. Even with the VA, I think a ton of veterans don't know you can set up a mental health plan involving your guns, and neither the VA, nor anyone else involved will seek to legally and permanently remove them from one's possession. So long as the threat is only to yourself, you ultimately remain in control of your firearms. Of course, once someone is feeling worse they'd be more willing to take the chance, but by then it could be too late.
This honestly needs both enacting the policy and running information campaigns where it's already policy.