In SA we already have something called Payshap, it's where the central bank acts as the intermediary. Because they do not handle transactions they hand this off to banks to offer the service. This service is free to use i.e. You can instantly send any cash amount to someone else in South Africa, up to R5000 per transaction and R30k per day. For free. The phone number acts as the wallet address and the wallet itself is the registered bank account.
It's like crypto currency already but the central bank is the main one. Imo when CBDCs come in, they'll be doing the same, just on chain with a scalable protocol.