Quote from Martinghoul:
There would have to be a mechanism to limit their size and prevent excessive concentration, though.
I rather suspect that if we had a formal "no bailout" policy - and actually stuck to it - the problem would largely self-regulate. But I'm not sure it's possible without also modifying the Fed's SOP, since they provide a backdoor bailout mechanism.
Anyway, this is likely all rather moot, since as a society we're simply not willing to do this, and I see little indication that is going to change.