*shrug*
I doubt it would work in an anonymous setting. Banking depends on trust.
I'm assuming the "men with guns" means the government. Societies find all sorts of interesting solutions for contract enforcement, and settling peacefully is usually cheaper than going to war.
If you trust the bank enough you could have an anonymous account just controlled by a private key. IF you trust the bank enough (big IF, but there are some examples in reality).
So we would all need to accept "their books" as legal tender
Stop trolling. That you engage in some contract with the bank does not mean their notes become legal tender. IT just mean that you accept them, not everyone else. Legal tender means that the bank notes are forced upon everybody.