There is currently talk of creating a National Bank to serve as toxic trashcan for the banks funded by the taxpayer.
I've got a better idea. How about the US create a National Depositor's Bank. A non-profit institution who's sole purpose is to hold deposits. No interest would be paid and a small transaction fee charged to cover operational costs.
No loans would be made, no debt purchased, sole assets would be the deposits.
Any commercial banks that survive can do the rest of the business, but no FDIC coverage, no federal funding or bailouts.
That way deposits at the depositors bank are always secure as the bank is unable to fail. No need for FDIC.
No need, ever to 'rescue' other financial institutions. So no socializing of losses.