Without deposit insurance there would be a crash of the banking sector

There is no reason to value bank deposits unless we are forced to pay taxes.

A good organisation would not allow the banking sector to inflate the money supply, it would protect its citizens from this type of inflation. Only a Government can allow ostensibly private firms to cause inflation, it cannot be done without (the threat of) force as people would reject this type of money as worthless. It is because the Government can issue money by fiat that it is able to extend this ability to private firms. If fiat currencies were (only) valued for their inherent value and not because of violence then banks would not be able to cause inflation. Banks are able to cause inflation only because Governments are able to 'create' value, they would not be able to do this except for the fact that fiat currencies are not chosen. If fiat currencies were voluntary and not forced then banks would not be able to cause inflation, deposit insurance hurts people because we are forced to value paper currencies, and hence we are then also forced to value bank receipts. Without taxation banks would not be able to inflate the currency.