Poor people don't use/waste electricity in large volumes because they are poor and don't have money to waste.

Rich people can waste enormous amounts of electricity and not be financially affected. It benefits rich people to schedule running the two clothes washers and two clothes driers at off-peak rates. Poor people don't have energy fat like this to cut.

This is about moving usage around the clock, not cutting unnecessary usage.

Yes, poor people have less usage to move around in absolute values, but they have more relatively to their income.

If poor people don't have much to timeshift then it doesn't much benefit them. A single parent working 1.5 jobs and then juggling laundry hours may not be useful for that family nor for society. Maybe the first nnn kilowatt hours each month should be flat rate - like minimum wage sets a floor likewise exempt some small base of electricity usage from the pricing games.