> a proof of mental sanity
A "proof of mental sanity" would be a far more concerning overreach than 3D printer bans or gun bans, especially as we see things which are mandatory in a society become something tantamount to personhood. I don't really know how one would even envision implementing such a thing.
Can you get a driver's license if you're visibly insane? The same standard should apply to getting a gun. A gun is comparably lethal.