You're completely missing the point. Undercover stings can happen even without a UBC. If an undercover agent tells a seller that he won't be able to pass a background and the seller still sells, then it's already a crime, even without a UBC law.
Do you see the ATF going out to do that now? No. So... what exactly would be different?
Perhaps it's also because the ATF would have to know about the seller before even setting up a sting. Not every shady gun seller is going to post a suspicious ad on craigslist or somesuch. A lot of those kinds of shady sales are going to be word-of-mouth. Even if the ATF somehow knew about every potential private gun seller, there isn't even remotely enough funding and/or manpower to perform that many stings operations.
Sorry, your entire concept here is utterly ridiculous.