If banks are funded by the government (ongoing bailouts and ridiculously beneficial laws for them) then they should be considered a public service and available to everyone, at least at a basic level
There's already the national treasury, it's why Aaron Burr killed Alexander Hamilton, he thought creating it created the exact same system that England had set up and was the whole reason we fought the revolutionary war. Aron Burr said that the creation of that bank made Alexander Hamilton the first real traitor to the US. Your just not rich enough to use the National Treasury as a bank.
Dude, Andrew Jackson dissolved the central bank that Hamilton started. The US wouldn't have a central bank again until the foundation of the Federal Reserve in 1918. Like, did you start this conspiracy after listening to Hamilton?
And the national treasury is something entirely different than the central bank that Hamilton established.