Frankly they should be, as this is the de facto situation that has been created. Extend the FDIC's scope to all accounts. Create new tiers for larger accounts, with their own funds/levies based on their increased variance. Increase capital requirements on banks, and introduce criminal penalties for bank executives that blow through the capital buffer, lose customer deposits, and end up requiring the government backstop. The industry has created these entities that are too big to fail, it's time they were regulated as such.
In the United States before the mid-1930s, there used to be something called "double liability" where the equity shareholders of a bank could be assessed up to the par value of their stock holdings if the bank failed and needed money to pay depositors. I've always been curious but have never looked into the history of why it was ended at that particular time. Best guess is just that they were desperate to do anything to make it easier for banks to lend money in the 1930s. Or maybe the usefulness of the assessment was called into question when banks failed right after the horrendous liquidation of the Great Depression, and none of the bank shareholders had much of any real assets to assess.
