First thing to remember is that there are very few ATF agents out there compared to people buying guns. They are not interested in those honest folks with a few firearms, they are only interested in things that really stand out of the norm. They aren't going knocking on doors without some sort of reason.
That said, I work for an FFL, dealt a little with the ATF and can give a little insight on what actually goes on.
FFLs are required, by law, to report to the ATF and to local law enforcement any time an individual purchases more than one handgun at a time, or within five consecutive days. That report is required to be sent to the ATF and local LE before the end of the day. This is supposed to combat firearm trafficking. I don't know what kind of tracking they're doing with it, obviously they're keeping some kind of record or the reports are worthless, but it's not true registration of all firearms. The idea is if you're not repeatedly buying multiple guns of the same kind of gun and they're not showing up in crimes in other states, you should be safe from this report.
We also do traces of firearms regularly. These come to us from the ATF, they are contractors and do not know why they're asking for the traces, nor do we, but we are required to return these within 24 hours. They are requests for the purchasers information, the firearm information and the dates of the sale. These usually are requested due to the firearm showing up at a crime. This can be to try to find out who used it at the crime, but are also used to return stolen firearms to their owners after it is recovered.
These traces originate with the manufacturers, who tell the tracing official where the gun was shipped and through this paper trail will end up asking the FFL for the buyer information.
We also must comply with the ATF when they show up on our doorsteps to do an audit. They will do an official inventory to make sure that there are no missing firearms and that they are all logged into our books correctly. They will look over every 4473 looking for errors, even as minor as a single misspelling or a transposed number in a concealed carry or driver license number. They will cite us for every mistake, no matter how small and if the issues number too much, or too egregious, the FFL can get fined or lose their license.
What they do not do, is scan or create records of these 4473s. They may copy ones that have mistakes or issues on them, but it is to create the report about the FFL, not to keep records of the buyers.
Currently the administration is on a hunt to shut down FFLs, that is their plan of "legal" gun control. If there is no one to sell them, then people can't get them. So the above processes are things that FFLs are complying with in order to stay in business.
The thing is, most of the ATF employees are actually good people and many are on our side. It's unfortunate that the top bosses are the ones that have the agenda and are filtering it down through the ranks who are just doing their jobs. You can argue that they have a choice and are are just "part of the problem" but not everyone can just quit their job due to political reasons.
The ATF does suck and certainly skirt the rules and laws in a lot of ways, but the majority of them are ok people and they do not have tens of thousands of agents that can just knock down any door. They are picking out things that stand out or people that cause them to take notice. There is certainly more to the story above than just a guy buying a few guns and have the ATF show up at his door.