Yeah, but the once a week cases are handled by a connection to the grid, just as at present. The bulk of the necessary time shift is handled by the battery and some other techniques to shift demand, and the rest is balancing contention between households in aggregate, and nudging storage and peaker plants, that is, exactly what currently occurs on the grid.
> As for shifting our day's schedule around electricity rates, good luck bringing that idea up with my wife.
The electricity costs of washing and drying are significant, could easily be hundreds of dollars a year. If you could save half of that by generally running a programme overnight, lots of people would do it . Not everyone would be able to because of noise, with that number increased by technological developments in software and hardware specialized for that use-case, but a lot of people would. And you wouldn't do it for every wash, only when it was convenient. This already happens over here, I often run my dishwasher overnight when the tariffs are lower, it's good for the environment and saves me money, or when I need it sooner I run it straight away.