Especially in contemporary times banks make money in an immense amount of ways that don't involve touching customer funds: debit transaction fees, international exchange rate "adjustments", ATM fees, the million 'special processing fee' type fees, and so on. In other countries I've even had to pay a fee when depositing, which was quite odd.
Of course this all is going to pale in comparison to the amount that banks make by d̶u̶m̶p̶i̶n̶g̶ ̶c̶o̶n̶s̶u̶m̶e̶r̶ ̶f̶u̶n̶d̶s̶,̶ ̶h̶e̶a̶v̶i̶l̶y̶ ̶l̶e̶v̶e̶r̶a̶g̶e̶d̶,̶ ̶i̶n̶t̶o̶ ̶h̶i̶g̶h̶ ̶r̶i̶s̶k̶ ̶a̶s̶s̶e̶t̶s̶
responsibly investing deposits. But of course banks under '100% deposits maintained' type systems could then engage in more typical behavior with their own funds above and beyond what's made from deposits. Under such a regime no bank would ever be "too big to fail", customer deposits would be 100% guaranteed at all times, and more. In exchange you'd see substantially slower overall economic growth and monetary multiplication, but I'm increasingly convinced that would not have been a bad thing.