Money is cotton. It can be washed and dried and ironed. Yes, it will eventually rot if constantly exposed to moisture, but if you've got it in your pocket, you don't need the (closed) bank or the (no power) ATM.
When the local grocery store was without power for a week after a windstorm (and it did stay open), they operated on cash and handheld calculators. The generator produced only lights.
As Lt. Gen. Honoré said after Katrina: "You need to prepare for the worst-case scenario, not the best-case scenario". Unfortunately, most people, businesses and governments prepare for the best-case scenario, and if that's not the kind they get hit by, they've got a world of problems.
Sue