Wholesale prices for electricity certainly vary, but consumer prices are a flat rate, 24/7. Nowhere I've lived has this not been the case, and there is no incentive whatsoever for consumers to time-shift their electricity consumption.
A huge part of what caused the Enron California electricity crisis is the utilities were unable, by law, to adjust consumer prices as wholesale prices changed. The utilities were required, by law, to provide whatever consumers demanded whenever they demanded it, at a fixed price, regardless of what it cost the utilities to provide it.
If this has changed in California, that's for the better. In Seattle, the price of electricity is the same, 24/7.
Consider gas prices at the pump. They vary every day, based on demand and supply of gas. Gas prices go up over Memorial Day. They go up when a refinery burns down. They go down in winter when people drive less. It works very well at matching up supply with demand.
It broke down completely in the late 1970's when the government imposed price controls and allocation controls at the pump. When Reagan repealed all that, things worked fine again.