How do you -enforce- the registry? That's the key problem, you'd have to search door to door, constantly, to make sure people weren't hiding guns. In Canada, not a "non-compliant society," with decades of mandatory registration and tighter sales controls than the US, the RCMP admitted there's still nowhere near total compliance. Per the Small Arms Survey, even in Europe the century-old registration schemes are, at -best-, capturing less than a third of otherwise legally possessed firearms and of course absolutely miss all smuggled firearms.

Here, the 5th Amendment prevents prosecuting a prohibited person, the ones we need to worry about, for failing to register as that is self-incrimination. In any event, there's no evidence that unknowing sellers selling to prohibited persons is a significant source of criminal firearms.

Registry's cost a lot of time and money to maintain, and put personal information at risk, but there's no proof they provide any crime or public safety benefits.