Fractional reserve banking is not a Ponzi scheme

If fractional-reserve banking is something different from fraud then all of the participants must be aware of how it works... and subsequently aware of the risks involved. This means that it is more like a pyramid scheme than a Ponzi scheme. With a Ponzi scheme the investors do not realise that their returns are based upon more and more people joining. There is an element of fraud involved in a Ponzi scheme which is absent from a pyramid scheme.

"Promoters also try to minimize withdrawals by offering new plans to investors, often where money is frozen for a longer period of time, in exchange for higher returns. The promoter sees new cash flows as investors are told they cannot transfer money from the first plan to the second. If a few investors do wish to withdraw their money in accordance with the terms allowed, their requests are usually promptly processed, which gives the illusion to all other investors that the fund is solvent."

If banks have deposit insurance then fractional-reserve banking (where the bank is insolvent) becomes nothing more than the counterfeiting of state liabilities. If the banks are not guaranteed then they can fail and fractional-reserve banking (frb) is a pyramid scheme. In a free market frb is a pyramid scheme.

If we assume that the debts will not be monetised when eventually the deposit insurance is tested by the depositors then like all pyramid schemes frb will fail. The banks will not be able to pay back the money they owe and they will fold... leading to hyper-deflation in prices.

Either the banks will fail or there will be significant monetisation of bank debts.