Do you have some data for this statement? (in the US, post FDIC deposit era)
Because even when a bank fails, there is usually more than enough to cover depositors, and what the FDIC does is arrange for the bank to be taken over by a healthy bank, with the deposits migrated (but equity and bondholders can take a bath). E.g. no depositor lost a penny in the financial crisis of 2008 -- which was the biggest financial crisis since the Great Depression -- even if they had money in excess of the limits. However it's quite unusual to have money in excess of the limit -- if you have that much, you wont keep it as a deposit, you'll hold some government guaranteed bonds like agencies or treasuries. It is extremely poor cash management for an individual to have more than 200K in a demand deposit account when they can be earning more with government guaranteed bonds that are just as liquid as cash. You can even open an account with Treasury Direct.