In the grand scheme of thing, missing a rent or mortgage payment does a lot more damage than the potential for overdraft fees.
"The "biggest check first" policy is common among large U.S. banks.. Banks argue that this is done to prevent a customer's most important transactions (such as a rent or mortgage check, or utility payment) from being returned unpaid, despite some such transactions being guaranteed.
Consumers have attempted to litigate to prevent this practice, arguing that banks use "biggest check first" to manipulate the order of transactions to artificially trigger more overdraft fees to collect. Banks in the United States are mostly regulated by the Office of the Comptroller of Currency, a Federal agency, which has formally approved of the practice; the practice has recently been challenged, however, under numerous individual state deceptive practice laws.
Bank deposit agreements usually provide that the bank may clear transactions in any order, at the bank's discretion."
Overdaft protection is cheap and easy to link to a checking account.