Well, the payment system facet of the banking sector is so tightly regulated by laws and central bank regulations that you could as well consider it controlled

Well, the payment system facet of the banking sector is so tightly regulated by laws and central bank regulations that you could as well consider it controlled by a single entity - the government. Nothing much changes, and in fact you can provide by law some basic rights of access to the financial system. Currently, in most countries it is conceptually possible for an individual to be rejected by all commercial banks without compelling legal reasons.