All of which can be achieved with advocacy instead of hardline laws intended to criminalize and deter gun ownership. Encouraging someone to seek professional training, to store their firearms safely according to their circumstances and teaching their children how to shoot and handle firearms safely goes a lot further than introducing more draconian laws and punitive measures.
I think without a rule many won't ever do it. But the rule doesn't need to be hardcore. You don't need a registry.
Just require anyone buying a gun to show a certificate that they completed a safety course taught by an accredited firearms instructor. The NRA could even be the accrediting agency, and the course could be taught on site in the gun store. People who learned from their parents could get the certificate by testing out instead of taking the course. A couple of hours is enough to teach ACTS/PROVE with some hands on practice, a demonstration of how to deal with a jam or squib, and a video on safe storage is enough. People purchasing a pistol should learn how to holster and unholster without shooting themselves in the leg, etc.
No need to have the police keep a copy of the training results like in Canada so it isn't a registry and by letting an industry group like the NRA accredit instructors you won't get the BS that happens in Canada with artificial limits on the number of courses. Let people get their certificate and directly purchase without waiting for a letter back from the police, etc.
And while some people might fake a certificate or cheat 99% would take the course, likely find the course a valuable one anyway, and a lot of accidents would be avoided.
That is what a reasonable gun policy would look like but given how politicized the issue is, I doubt it will ever happen.
You can also implement background checks without a registry. Police could issue you a verifiable certificate that you have a clean history without knowing whether you were using that certificate to gain employment, buy a gun, or coach a kids sports team.
FFL would then just check that you have both certs and let you walk out with your purchase.
It is totally possible to create reasonable gun SAFETY policies that aren't gun CONTROL policies.