The 4473's aren't filed by the buyer's name, but by the date of disposition. Compiling a database from that would be random, laborious, and full of holes.
Well, if you have unlimited resources, and "close enough for gubmint work" is good enough (false positives can still generate arrests and prosecutions, after all- "Of the Lawyers, By the Lawyers, and For the Lawyers"!) .....
It does not have to work as advertised, it just has to encumber gun ownership, complicate the business of selling guns, create more sinecures for gubmint employees, and generate more business for the Legal Profession/"Justice" system ...... and the politicians get to say they "did something" ..... where is the downside for anybody but gun owners and those selling guns? When government mucks with the Free Market, it is always the folks using the product that suffer.