Monumental resources
Yes, the .gov has monumental resources - but to large extent - the resources are like the Post Office or the DMV. That level of motivation and efficiency.
There was a post recently about a plausible scenario of the government eventually outlawing and confiscating all privately held firearms. Perhaps the government could sift through all available 4473's. Since this happens incrementally, they track down owners of "bad" guns first, but later get to those with sporting guns (evil long range sniper). And sure, they could start sifting through Walmarts credit and debit card records to see who was buying what ammo, and all the public ranges to see who came to shoot, interview "known former gun owners" for who else they knew of.
Plausible maybe, but involving years of effort probably crossing more than one election cycle, enormous computing power that the government seldom seems able to manage well, a bureauracracy of thousands of efficient and motivated workers. That's my point.
I prefer a private transfer, but if an FFL has something I like I don't hesitate to do the paperwork. If I have cash for ammo I use that but I'll whip out the debit card if I don't.