It could very easily do that. Try writing a check for a million dollars - the bank won't pay it, and the same if you try using your debit card for very large amounts. Visa/Mastercard/others request authorization from the banks before they authorize payment. The banks choose not to link the authorization directly to the customers balance, thus allowing them to spend more money than they have while paying the bank a $34 fee for $4 coffee.

Banks can make money in other ways - in many parts of Europe banks don't charge overdraft fees - they just charge you a monthly fee to cover the cost of providing service. Other banks (e.g., ING Direct, Uno-e) in those same countries provide accounts without fees, and without access to a branch network. You can choose what service level you want without being screwed over by the bank.