I think the more coherent thing to do would be to treat banks like other industries and not bail them out. Customers would then place their money in safer banks, discouraging banks from engaging in risky behaviour.
Sure, I'm convinced that no one is going to riot when they get their their lifetime savings casually wiped out. I bet on them fully understanding that they just made a terrible decision when they chose the wrong bank, it's entirely their fault and that it is what's best for the economy as a whole.