They can't allow banks to fail because that is how money is created. In essence they would kill the money making mechanism.
Quote from Troy McClure:
This is a good question and I haven't heard anyone in charge answer it well, maybe someone has.
"Too big to fail" is the usual answer, but why? Bernie Sanders (I-VT) said "A bank that is too big to fail is a bank that is too big". Amen.
Perhaps it is all money down the rathole either way. If the FDIC takes over the bank depositers will need to be paid. Banking-business relationships will be destroyed. Too disruptive.
OTOH, if you could get past one hell of a month, new banks would start popping up everywhere.