That is a market problem not a regulatory problem. How businesses make money is determined by the price system.
Banks would have to survive like any other business and charge for services.The banks would actually have $1 of cash for every dollar they owe to their customers: there would be no chance of a harmful run on the banks
No, there wouldn't be any chance of a bank run, because there wouldn't be any banks. Few, if any, people would be willing to pay a large enough monthly fee, for a bank to be willing and able to keep it for them.
Your mattress is 100% reserve. Not safe enough? Buy a safe.