In order to sell a car be it dealer or private owner, in America, you have to transfer your title to a federally mandated state registry, before registration of the vehicle can be given to the new owner.
A private owner to someone else, there is no record of transfer, nor is there a record of transfers beyond that, it could cross state lines to a state where registration is not done or just not registered legally anywhere, and only discovered as illegal after a crime is committed. Discovering how this individual acquired the weapon would take time, which could be spent on other cases.
With a title of ownership and required title transfers to new owners, it would expedite the investigation into such things as gun smuggling, illegal weapons and potential threats and terrorist organization.