Why is it so easy to buy a gun?

In order to buy a gun, you have to go through background check. What does this background check consist of? Name, address, driver's license number all to the FBI and they give you the go ahead or they say nope. Additionally, gun owners must fill out a 4473, a basic questionnaire involving name and address, optional social security number and yes or no to questions like "Are you an unlawful user of, or addicted to, marijuana or any depressant, stimulant, narcotic drug, or any other controlled substance?" Where does this form go? It stays with the person who sold you the gun in paper form for 20 years. If the gun did happen to be used in a crime, law enforcement would use the serial number to contact Remington who would tell them the distributor. The distributor would then direct them to store where it was sold. While the concern exists for gun owner privacy, if the FBI had records of who owned guns then if they were to spot suspicious internet activity they could appraise the risk of them killing someone better. For example, the shooter in Florida had posted online and been reported for saying things online about his desire to be a school shooter. This small change of sharing gun owners information with the FBI could bring about big changes. Do you think this should be enacted? Is there another solution to this problem?