I am not a professional economist, but this one seems relatively obvious to me: There are self-amplifying effects relating to monetary velocity especially in a fractional reserve banking system (which dates back to goldsmiths), e.g. people try to hold money, velocity goes down, the price of money goes up, people can't pay back debts, debt is destroyed, in a fractional system this decreases the money supply further, etc. Velocity of trade is a public good and commons problem because if I refuse to trade with you, e.g. I don't buy your apple for money, I only lose the part of the gains from trade which would've gone to me, but you lose the portion of gains from trade that would've gone to the apple store, and then the farmer loses the gains from trade with the apple store, and can't buy a tractor, etc. Money is a tool in the first place for allowing trades like this, and in the presence of sticky prices and nominally-anchored contracts and debts, decreases in the money supply can cause your economy to lurch some of the way toward its state if cash had never been invented, which is bad. If you regard money as a tool to create velocity of trade, and systemic velocity of trade as a public good, the rationale for central banking seems relatively clear: It is to create the public good of money with a predictable price path, or in the Sumner version, create a predictable level trajectory for nominal GDP.

It's possible one could transition to a system of free banking now that we have much more fluid markets, but step one would be to outlaw fractional reserve lending and require banks to create bonds or bond-equivalents when depositor money is invested in them, rather than allowing banks to falsely claim that depositor money is always available on-demand in which case black swan bank runs can blow up the system, requiring an FDIC. You have to get rid of the public good rationale for an FDIC before transitioning to a system of private insurance on bank bonds where the price signals of insurance cost will exist. You will recall that it was the problem of runs on banks (and the subsequent fractional-reserve money supply decrease and deflation) which originally led economists to think central banking was better than the alternative. Even so, it's not obvious to me that self-amplifying velocity effects couldn't be awful (price of money goes up, people want to hold more of it) even in the absence of fractional reserve lending.