One issue with this is that at we have peaks in demand for electricity exactly when cars are more likely to be on the roads (morning and evening commute times,

One issue with this is that at we have peaks in demand for electricity exactly when cars are more likely to be on the roads (morning and evening commute times, roughly). So for it to happen at large scale, we would need to see significant reductions in eg night time generation capacity. In my view this is unlikely (nuclear and wind will still run at night even if we close every coal, oil and gas fired generator).