This is its best feature. It would simply end banking as storage of money also - banks would have to pay more interest if they wanted to compete against zero-interest but absolutely safe government money market checking accounts. There'd be no public interest in the government insuring them anymore, either.
Instead of choosing a bank, most people would be looking for access to the widest network of broker ATMs.
We could solve this stuff with very centralized postal banking also, so the crypto part ultimately isn't super interesting for me unless it solves some scale problem relating to speed of settlement, costs and/or allowing untrusted middlemen.
This really would crash the utility of transfer apps like Venmo to zero.