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A central authority doesn't control the size of the money supply in our current economy either, as the vast majority of money is created by private banks and other institutions issuing loans.

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Those “private banks” are at least in theory heavily regulated by the central bank. The central bank controls interest rates and thereby the cost of money. They control the amount of base money in the system and they control the reserve ratio of “private banks” thereby controlling the amount of leverage banks can apply to deposits. A central bank most certainly controls every aspect of the money supply.

Notably, the Fed set the reserve ratio for banks to zero percent in 2020 which absolutely contributed to this latest banking crisis. I am a bit surprised this hasn’t been mentioned as a contributing risk in the media, well not that surprised. [0]

[0] https://www.federalreserve.gov/monetarypolicy/reservereq.htm

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