Money is no more than whatever the Government thinks that it is

There is no definition of money which is not satisfied by bank credit, with the existence of deposit insurance.

The only reason there is not a run on the banks is due to the insurance. Without the insurance there would be a run on the banks.

We don't need deposit insurance (to maintain the stability of the banks) all that is required is for the Government to recognise bank deposits, just as they do with cash. If the laws to do with legal tender are extended to include bank deposits, deposit insurance can be removed without consequence. Removing deposit insurance would make no difference in those circumstances. If the Government does not (seek to) recognise bank deposits as money then it makes no sense to provide deposit insurance. Deposit insurance means that banks can print money, for money is nothing more than what is recognised by the Government, it is only what the Government thinks that it is.