I've got the science to prove this isn't the case in the Pacific Northwest.
When I got my masters in water resources management everyone was saying this. It isn't true.
*Certain places* will suffer extreme shortages. California is a bad example because 80% of the water goes to agriculture under an archaic water rights system that gives almond farmers an incentive to use wasteful flood irrigation while their neighbors go dry.
Waste is the problem everywhere, not hard shortages. Have fun trying to use water as currency outside of the Fallout universe. Ever tried to carry it anywhere? It's heavy.