Sounds unenforceable.
PP sales are meaningless without registration, but once they get universal background checks, you can bet we’ll see registration after the next mass shooting.
First thought that entered my head.
Not just unenforceable.
Unintended consequence: once a gun is sold off-books, it will have to stay off-books. When it pops up in the system again, lack of a purchase record is presumptive evidence of criminal acquisition. There is no incentive to bring a gun back to “legal” status, but the nontrivial cost (hundreds or thousands of dollars) and robust durability mean the owner isn’t just going to trash it and has an interest in selling it somehow.