I work at a different bank. The rates charged to banks for FDIC insurance have been based on the assumption that the FDIC would cover depositor losses up to the insured limit. By choosing to cover all losses even above the insured limit, we have chosen to put the burden for paying for those losses on all of the other banks (and indirectly on those banks depositors). I suspect this means that you will not see the interest rate on savings accounts go up as much as it might have otherwise.
I'm not saying this outcome is terrible, perhaps it was the best solution for the system as a whole. But using an insurance fund to cover a kind of loss, the insurance was not sized to address is not a choice that has no impact.
If I were in charge of everything (perish the thought!) I would probably have insisted that the uninsured portion of the deposits take some haircut. If depositors had gotten back 90% or 98% of their deposits instead of 100%, it might have increased the chance in the future that institutions with 100 million+ bank accounts would pay more attention to the risk profile of the banks they choose to invest with. Banks are rewarded mostly in proportion to the risks that they take; having a force other than government regulation that pushes in the opposite direction can be very useful.