As Alexx says, there is still *some* risk, although it's more diffuse.

More to the point, though, FDIC is a fine illustration of what I'm talking about. Bank-panic behaviour is so consistent -- almost predictable -- that the FDIC was created as a specific mechanism to tamp down the effect. But I don't hear much about these sorts of tools at the theoretical level, despite how clearly effective it is, and I suspect that's because it *assumes* herd behaviour that traditional economics doesn't talk about very much...