State owned banks are usually a bad idea for one reason, corruption. Historically, having the government control money supply is usually a recipe for prolific corruption. A good modern example is Turkey.
While corruption is never good, I’ll take private-sector corruption over government corruption every day of the week if I’m forced to choose. Governments are sovereign.
The government is corrupted by its relationships with the private sector. The only other way to pull money out of government is through salaries, and government workers don't get paid that much.
Most people are “the private-sector”, it’s called society and includes every voter not working directly for the government, which is most of them. If a government is necessarily corrupted by its relationships with the private-sector, then the word corruption is meaningless in the context of government. You should also mind that governments can also be corrupted—can be but not necessarily are-by their relationships with their own employees. I advise you to find and apply a limiting principle, one that would be useful for you in distinguishing government corruption from government business.
Corruption comes in sorts of form, is unavoidable, and is a very grey subject. It’s a tough balance between growth and exploitation. But historically, government rooted corruption tends to be harder to remove than “buying” politicians” which the rich and banks do nowadays. Stanford has a really well explained thought process on this on their online philosophy library.