I worked at a company for a while trying to make a battery control device that predicts the peak daily demand and discharges the battery to offset it.
It's kind of crazy how much money you can save by shrinking your peak demand during the time of day it's most expensive.
Where I live, hydro is the dominant power producer.
My electricity costs 40% less from 11 pm to 7 am and 30% more from 4 pm to 9 pm.
A hydro dam can also be thought of as a battery. When you are not using it, the dam fills up (charges).
My utility buys inexpensive excess power from the NA grid when electricity is cheap and drains the dams when third-party electricity is expensive. Adding other renewables to the mix plays a similar role. The pricing incentives shrink peak demand as you suggest.
One of the reasons residential solar is a tough sell for me is that electricity is relatively inexpensive and likely to stay that way.