The state is not a bank

If there is deposit insurance this means that banks are like the government and cannot fail. But there is no reason for the state to protect the banks in this way... banks could be like any other business and capable of collapse. The existence of deposit insurance indicates that the state considers banks to be like itself and of privileged status. But there is no reason for the banks to be part of the state. Banks and the state can be separate.

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.

The law is not a consequence of the state

Property rights are established when someone uses force to protect a particular area or object. This means that property rights are always concerned with the opinion of people with regard to whom has the 'right' to occupy a space or have use of an object. The government is often asked to intervene when there is a property dispute such as a burglary. But it is an illusion to think that without the government there would be no property rights. After someone has been arrested for a crime (such as burglary) they may go to gaol or they may be released. It is clear to most people (certainly in 'developed' countries) that the government is far more lenient towards criminals than the average person would be. The people at large are perpetually frustrated by the government when it comes to matters of justice. The government intervenes to prevent an escalation of violence (which has its merits) but too often the end result is that there is no justice at all and the offender is released without consequence. In an anarchist system there would be no government to intervene in the dispersement of justice and people would not be able to violate property rights so easily. The government is a detriment to property rights because it prevents people from protecting themselves. If criminals are released there is no rule of law... as there would be in an anarchist system (criminals would not be released prematurely). Government is a detriment to the law.

The problem with banking is socialism

It might be a nice idea to think that when we place our money with a bank that it is guaranteed and certain to be returned. To make this guarantee possible we have deposit insurance which is a form of socialism whereby the liabilities of most banks are protected by the state. But this form of socialism - like all others - does not come without a cost which manifests elsewhere. There are (negative) externalities to this largess by the government. The result is that the value of existing units of currency is diminished because the guarantee of banks means that eventually there will either be more banknotes or there will be a default of the banking system. Whilst it might appear harsh and uncaring it would be best not to guarantee the banks (and their savers) from failure... this means that all deposits would be made at the risk of the saver and no other person. This kind of individualistic approach to banking and investment would mean that banks would not be able to disrupt the rest of the economy with inflation. It would be best for the rest of the economy to remove socialism from the banking sector.