Databases are management headaches ...
There is another issue ... maintenance of all this data.
Think about how complicated this is, currently. They may know, in various ways, who has bought what gun(s) over the years. However, there are changes in address, people die, people get married and change their names, guns are stolen and sold, guns are purchased privately, etc., etc.
Clearly, various people and groups want to help the BATF improve their recordkeeping ... including the MMM, NEA, Handgun Control, etc. But, until they spend billions, change the laws and force everyone to comply, their data is spotty. Look at the current mess in Candada, and as I recall, they have only 1% the number of guns found in the U.S.
The feds still have more data than they should, but I'd wager that BATF agents would admit privately that their databases are pretty mediocre. Right now, I think the threat is usually overstated.
Regards from AZ