There is a distrinct problem in that, actually doing a per person background check on a per instance basis is incredibly costly. With typical bureaucratic inertia, you are looking at 3-5 mandays per check. At around $250-500 per manday in cost.
https://www.fbi.gov/file-repository/nics_firearm_checks_-_month_year.pdf/view
There were 2 million NICS checks in July.
Lets say that the amount of paperwork and a 2-4 week wait really suppress buyers, to 1 per 100, that's 20,000 Background Investigations. At 3 days each, that's 60,000 mandays (that's 1000 investigators to get it done in 10 working days) and, oh, $15 million in expense (before paperwork, filing, service fees, etc.) In one Month. At 1/100 the present purchasing volume. So, there's simply no way that is affordable in a sensible universe.
Which is why most of the "UBC" bills out there just assume all sales can be dumped on NICS. Which would require some process to either qualify people to have access to NICS, or set up a support staff to field all the F2F contact calls.
And that really puts into perspective the factoid about how the NICS records could be as little as 49% and maybe as much as 72% complete, of
known Prohibited Persons.
And, of course, this is after we leap over the logical hurdle of law-abiding criminals.