Though I wonder whether you could just get an account where your deposited checks just take a while to clear (when the bank actually has the money)? And where any attempt at overdrafting would just fail?
Basically, a bank account where the bank does not extend you credit. A purely 'pre-paid' affair.
I guess the kinds of people who would want these accounts are on average not good customers?
(I know that they have these kinds of accounts in eg Germany where I grew up. But your average German is averse to taking on debt; so you just get average Germans signing up, instead of the adverse selection you'd have in the US?)