If bank deposits are guaranteed it doesn't make a difference to people how solvent the banks are

People don't care about the solvency, or otherwise, of the banks if the bank is licensed and has a Government guarantee.

Given the choice between having cash and holding bank deposits with Government deposit insurance, from licensed banks, people are indifferent. People don't care about any of the perceived advantages of cash, if they (such advantages) exist. If the Government has provided a guarantee this is enough and customers are not concerned as to the solvency of the banking system, and there is no reason for them to be concerned.