Seeing so much news about blockchains and banks I have a question that I may need your help.

Taking in consideration the Bank Secrecy Act, can a Bank use a completely Encrypted Ledger? KYC is still required, deposits and withdraws will still be reported if one deposits/withdraws more than $10k. But the bank has no idea about users' balances or their transactions. So, the bank uses an encrypted ledger that doesn't have a key to be decrypted. Namely, the ledger is encrypted in a way in which transactions are encrypted and unlinkable. Only the users can decrypt their balances and spend their funds with a... hardware token. Using this hardware tokens users can give a proof to the bank that the balance was right. Something like how is done in blockchains solutions focused on privacy.

Can public/private banks in the future use encrypted Ledgers? If yes why banks didn't do it until now. If no, why banks can't use encrypted Ledgers?