Well, in a sense most of the big banks(especially BAC) do, with fee's everywhere. I don't know, it's not my problem, I bank with Navy Federal(a mega credit union) and don't even bank all that much(most of it flows out of that into my ameritrade account).
As for using banks as an emergency fund, remember that no bank can survive a bank run, so you should always have some means, whatever it is, of paying for things(credit cards, cash, etc.) to survive a short time-period(week or two) that systems might be down, or the sky is falling.
For any time period that the sky is falling that you don't have the reserves to handle, don't worry, you'd already be dead.