With how the system is supposed to work, isn't anyone who have uninsured deposits supposed to buy their own insurance? If the risk of bank failure is low, then

With how the system is supposed to work, isn't anyone who have uninsured deposits supposed to buy their own insurance? If the risk of bank failure is low, then the insurance premium should be very low. If the premium is high, that's an indication that the risk is too high and maybe you should find an alternative.