The water network can supply plenty of treated water in the early hours of the morning when demand is low and little or no spare energy is available at peak demand when people rise in the morning and return home in the evening. An affordable heat store allows water storage in homes at minimal cost. I worked for Anglian Water and other Water Companies for over 30 years. I was the most senior design Engineer in Norfolk with specific responsibility for water network design and construction, so I know that when you add 24-48 hours of water storage in enough homes, the effect on the water network and water supply would be game-changing. The effects on regional water supply and distribution would be:

Reduced peak pressures in the networks gives fewer bursts and less leakage in general.
Reduced magnitude in cyclic variations in pressure leading to fewer bursts.
Less energy would be needed to pump water around the water network
Reduction in the unit price of water because supply sources can run at a more even output.
An overall increase in water output from individual source works. 

Many source works have a minimum contact time for treatments and the maximum output based on those minimums. Without storage capacity, water is left idle in a process tank during parts of the day.