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if recharged at the wrong time make power generation a worse polluter
That problem is easily solved with a load management switch. For those who are not familiar with them, they are essentially a radio-controlled switch. When they get a signal from the power company's transmitter, they turn off for 15 minutes, and then automatically turn back on.
They are addressable, so the power company can choose which switches get turned off. During a peak load event, the local local power company turns off 1/4 of the switches at a time, rotating every 15 minutes, so that in an hour every switch will have been turned off once for 15 minutes.
The local power company installs them, at customer request, on electric water heaters and air conditioners. (They could just as easily install them on a receptacle for charging an electric vehicle, and I suspect they would do that NOW upon request). The benefit to the customer is that they'll come out for any problems with the water heater or air conditioner and fix minor problems such as a bad heating element or contactor for free.
There's an apartment complex nearby that has load management switches on every single water heater they have (about 144 of 'em).
My understanding is that these switches keep rates down by keeping the power company from setting a new peak record, which means that they won't pay as much for the electricity that they buy.