The banking system will exist as long as the states themselves exist, since they are part of each state. They will apply something new to the extent that it is economically beneficial for them.
Governments and central banks want something they can control, so it's very unlikely they'll build CBDCs within existing public blockchain networks. They might not even need to use a Blockchain at all, since everything will be centralized. A traditional database would be more than enough for banks to manage digital fiat currencies of their own.
Ultimately, we'll live in a world where both decentralized cryptocurrencies and the traditional banking system will power the mainstream economy. People will get to decide which type of currency to use from the other for day-to-day payments. While governments will not be able to take down crypto/Blockchain tech in its entirety, they'll be able to enforce strict rules in order to prevent as much people from using it. With how banks have gone so far, it's very unlikely they'll disappear anytime soon. Just my opinion