In fact, I was surprised that this WASN'T the main point of the FLC banking system. What I'm talking about is having all the banks working as one. You open up an account in Shady Sands and deposit money and you can withdraw your caps in the Hub etc. The current system of all the branches working in isolation is pointless.
The main point of a banking system in a post-apocalyptic setting would be to ensure the safety of your cash - instead of travelling loaded with caps and risking getting mugged on the way, you leave your cash in one place (we assume that the banks have their own efficient communication system) and withdraw it when you reach your destination, that's how it worked in the middle ages and I can't imagine why it wouldn't work like that in the Wasteland.