One of the largest gun registration systems in the world is the hunting license.
Get a large game license, they know you have a rifle.
Get an bird license, they know you have a shotgun.
The hunting license means you have a gun.. They know that much.
14.8M according to this 2015 report ( http://wsfrprograms.fws.gov/Subpages/LicenseInfo/HuntingLicCertHistory20042015.pdf ) And they know the names and addresses.
21.8 million Americans hunted at least once over the past five years ( https://www.nssf.org/PDF/HuntingLicTrends-NatlRpt.pdf ) And they know the names and addresses.
Etc.
CCW lists. Background checks. Store records. None of that ever disappears.