I can see the logic of that, "Let's act irrationally together and force the government to bail us out next time we make a run on our own bank." Or they can act rationally, distribute (manually or through existing methods) their cash across multiple banks so that their risk exposure is lower and they don't have to depend on the government maybe, possibly, bailing them out. You know, the thing they'd have done if they'd hired financial managers in the first place (which obviously they didn't, or they hired incompetent ones).

It's not irrational to act in your own interest. It's irrational to suppose that everyone should act in the majorities interest.

I'm not saying they should act in the majority's interest, I'm saying they should act in their own interest. Mitigate their risk by managing their capital properly instead of hoping ("Hope is a poor substitute for strategy") that things will work out. It's irrational to act in a way that, if a failure occurs, requires someone else to bail you out when they aren't legally or ethically required to bail you out. That's operating on hope, not strategy.

Putting all your capital in one too big to fail bank is the least costly option and the optimum strategy.

Until the US lets the largest bank fail this will continue to be the case.