Actually one must already go through a government check (ok, the bank does it) if you open a bank account or take out a loan (mortgage, auto loan, student loan, etc).

If the government believes you're a terry-wrist and your name is an on OFAC alert list, good luck with banking - it isn't going to happen.

This check happens behind the scenes, but is a requirement thanks to the Patriot Act. Not sure how many consumers are even aware of this.