Is the premise here a public or private/permissioned blockchain?

How would automatic bill payments work with a blockchain? How do lost wallets work? KYC and AML?

I do agree that blockchain like technology will become the foundation for banks and other financial institutions, probably even government finances. I have serious doubts that they will be public blockchains. Very few want their financial history on a public ledger for all to see. It will also be hard to get them all on the same chain internally, but there is probably a consortium that will merge to handle inter-chain transfers.