This will still put the baseline of the grid higher, just averages it out possibly taking more when its a good time. I think batteries should be hosted/hooked up by the power company, so they can attach them to a power management system. (I think that already exists)

I left out the "where will we get all this power" part, because that is already discussed a lot. I just wonder if the power grid will be able to handle this immense increase in usage, even if spread out. You still need to transport it.

edit: I think the powering down of offices and business makes enough room for the evening to use more.