If the central bank promise of deposit insurance is reliable* then banks print money

Deposit insurance from the state makes people relax about the solvency of their bank. Whilst a free market in banking is perfectly possible (with perhaps the problem of occasional small and insignificant bank runs happening from time to time) if there is deposit insurance then we should make sure to prevent bank lending of deposits.

If there is the promise of deposit insurance and fractional reserve banking (frb) is not illegal for those banks then one of two possible problems will emerge... if the promise is reliable and frb is not forbidden then effectively banks have been given a licence to print money. If the bank guarantee is unreliable then (because the false promise of deposit insurance gives people a sense of security with regard to their bank) an imbalance between deposits and reserves will grow leading to significant instability and the possibility of a huge crash.

If deposit insurance is given it should be given only to banks for which frb is illegal. If banks don't print money then the deposit insurance is an unreliable promise and there will be a huge financial crash. If banks don't print money there is no reason to not remove your money from most banks... there is no reason for there not to be a significant bank run.

*And there is no prohibition of fractional reserve banking.