The government has the tools needed to go after real criminals. The government does not make use of the tools it already has. It is much easier and safer for BATF agents to prosecute law-abiding citizens for 'paperwork problems' (e.g. misspelling a manufacturer name) than to go after real crooks. After all, real crooks not only are less likely to cooperate with police, but they're also likely to shoot at them.
One of the people convicted under the Brady Act was caught when he tried to redeem a handgun he'd pawned for some cash. His criminal record was clean except for a 20+ year old conviction of being an accessory to a robbery. IMHO, the government probably went after this guy because he was a 99.44% law-abiding citizen and they knew he wouldn't be dangerous. By contrast, there are places where gang bangers are well-known to be illegally armed and yet the cops do nothing about it.
Background checks are not about reducing crime. They're about giving the government a list of all the guns owned by law-abiding citizens. The government doesn't care about the guns owned by criminal gangs, since the government and the gangs are allies in the war against productive citizens.
Detroit has had a lot of children killed recently by stray gunfire in drug-related shootings. It's being called "gun violence". After a high-profile conference of "community leaders", politicians, and gun-grabbers, the Detroit police announced a new policy. In some precincts, police would "ask the felons we know who carry guns not to carry them any more".
You mean these people are known felons, they carry guns, and the police are going to track them down and ask them not to use guns? Whatever happened to throwing their ass back in jail?