You make a excellent point. Every legal purchase I’ve made through a gun shop, online store, regardless of a pistol or long gun required paper work filled out. Where that goes, who knows?
However, the gangbangers, thugs, Obama’s sons, call that what you will, won’t dare fill out any forms.
So if this really were to happen, the law abiding citizen would become cannon fodder for the rest. Maybe that’s actually be part of the Marxists plan.