They don't have to discredit them, the Feds are doing that.
Local banks, credit unions, etc are NOT on the "too big to fail" (or "systemic risk") list so therefore they can fail and will be allowed to fail.
It's also interesting that of the Big Four that are "too big to fail" three of them offer savings rates of under 0.25% it's almost as if they don't have to do anything to appeal to customers.