Yes, that's also being done. A critique I have seen is that this is empowering the rich to get richer. Renters are less likely to be able to adopt these strategies.
The rich certainly benefit more, like anything where an investment needs to be made (I expect the new plans will be like the existing 'free' power plans and be a poor choice without a battery). In this case, the poor still benefit a little bit as it should drive down peak period prices and the cost of fixed rate plans.