This already exist in some places (for example Amber and Powerclub in Australia).

The issue is it's more effort than most people are happy to exert. They are used to flicking a switch having the appliance on whenever they want it. To change that will either involve much higher prices, a substantial shift in the way we think about energy, or an improvement in technology to allow the load shifting to happen in the background without the user noticing.

We turn to batteries instead because it's easier to build something than it is to change behaviour.