[jampekka]

May depend on the country, but at least in Finland the account numbers have been unique across banks for ages. The first part refers to the bank (actually a branch at least back in the day) and the last part to the account within the bank. There was and is no need to specify the bank separately.

The mobile phone numbers had the same system. Three first numbers signified the operator, but the whole number it can now be transfered to another operator.

This is not hard stuff. The numbers aren't magic, they're just identifiers. We're not bound to mechanical routers or card sorting machines anymore.