Yes, see David Chaum's original pre-bitcoin "e-cash" and the more recent GNU Taler project: https://taler.net/en/
The problem is that banks won't implement these systems unless they're forced to. They seem to benefit from the insecurity, surveillance, and bureaucracy of the existing system. So we will have to make new banks...
Perhaps CBDCs (Central bank digital currencies) are close to what you're looking at, the concept being digital money issued and verified by a central authority. There's been a bunch of research done by the central banks of various countries e.g.
https://www.bankofengland.co.uk/research/digital-currencies
https://www.federalreserve.gov/central-bank-digital-currency...
This is just a vague example, not a working idea. The point of it is that the level of security and trustlessness is not always required to be absolute. E.g. even with fully-secure pow crypto we still have to trust non-crypto claims about usdt, [non?]shitcoins, “hot” wallets, and other maybe-not-ponzis.