Bernie Sanders recently stated USPS should offer banking services. While this may actually be a good idea. The target audience would be lower income families/people. Now this would not be the first time a form of nationalized banking would be offered. It has just been a few hundred years since it has been used.
Alexander Hamilton actually helped establish a national bank while the Unite States was being formed. Although it was later done away with by President Alexander. It could still be a good option. It could be run much like a credit union.