I understand where you're coming from.
The simplest answer is: if you don't want to bank with us, then don't. We don't imagine that we'll replace every bank ever. There are plenty of traditional banks that may be going bust left and right, but hey, you're free to do business with them.
A more complicated answer is that BankSimple will have the backing of established, traditional financial entities who are fully FDIC insured from the get-go, so the risk to you as a customer is quite low.
There's no such thing as banking without risk, but I understand why you feel drawn to more traditional financial institutions. They certainly do a good job of marketing themselves as stable and dependable.