But then how do you explain bank runs? If banks practice normal lending, then bank runs shouldn't be harmful, because the bank would always have enough money to redeem all deposits.
It's also worth pointing out that bank runs are incredibly rare events. In a correctly functioning market, a bank can always pay its depositors by securitizing its loans. In a dysfunctional market (such as now) there are usually government guarantees that help smooth the process. The big problem with banks at the moment is that they have been keeping insufficient capital to cover their losses. Insufficient reserves has not been a problem.