Banks as private middlemen providing society with a payment system is an outdated and baroque system. Today, the whole payment system of an average nation can work over a single cluster of computers in the basement of the central bank, there is absolutely no reason not to provide this service for free to all citizens and businesses since it's a critical part of living in a society. The whole superstructure of banks, credit card companies, payment processors etc. can be vanquished with one blow, by issuing every citizen with a digital identity card which can be then used to access his free accounts provided by the government, no other paperwork necessary. Some resources should be spent on preventing laundering and fraud with the system, but this needs to be done in the banking system as well, with the costs passed on to the consumers.

I disagree with some of the other claimed benefits. Central bank accounts holding monetary base would not offer interest, just like paper money, and will always offer negative real interest when considering inflation. The government pays interest when borrowing from the banking system, and you can certainly use your central bank account to buy these securities (just like banks do today) but then you are no longer holding the risk free monetary base, you have a security with some non-zero risk of sovereign default.

The stability of the system is also not a given. Commercial banks run the payment system as an ancillary to their main function, and that is to match un short term liquidity, that is temporary savings and surplus of people and firms, and redirect those resources to long term investments. This is a critical economic role and for the economy to work it will still need to be provided in some other fashion, for example by a credit market.

This already happens to a large degree, for example banks offer mortgages and package them into securities that are sold on markets. This whole MBS process was behind the financial melt-down in 2008, since these practices were less scrutinized than the direct loans and deposits of banks. In fact, both are the same process: monetary base increases in velocity and is multiplied in the form of interest bearing securities that represent investments in the productive economy. The stability of the whole financial system is predicated on the quality and diligence of these investments, and credit markets proved to be notoriously bad at discovering this.

One thing to note though, is that when a "bank run" happens in the "shadow banks" of the credit markets, the bad securities are wiped out but the goods ones quickly recover. So the central bank can ride a financial storm by blanket buying paper with fresh money and let the market discover the winners and losers. Bank runs are self-limiting because securities drop to a value where they become enticing to value investors. When commercial banks are involved though, you have massive contagion since bank runs are self-fueling, once a bank is in trouble every investors starts to request their money, even if the fundamentals of the loans made by that bank are sound in the long run.