The problem of course is when you allow too many "too big to fail" institutions to exist and suffer a cascading failure such as the ones started by Creditanstalt in May 1931 (http://en.wikipedia.org/wiki/Creditanstalt) and Lehman Brothers in September 2008 (http://en.wikipedia.org/wiki/Subprime_crisis_impact_timeline...), the latter fortunately got stopped.
One obvious solution is outlaw "too big to fail" although that seems to be hard (the current US financial regulation bill enshrines them), and it still doesn't address the lemming like behavior you see in bubbles which allow near total systems failures.
In fact, wasn't the US banking system of the '30s mostly comprised of small banks (as I recall, 8,000 of them had failed when FDR closed the rest, but my memory of that number could be off or maybe that was the total???).
Rather than trying to avoid pain, we should acknowledge failure as a part of a healthy free market system and optimize for a robust system that can handle failures instead of having "too big to fail."
It should be like when circuit-city falls, there isn't much damage to the economies, instead of the fear that comes from when financial institutions are failing.