Where I live, at 6200 feet, we have oodles of sunshine. Even so, the air-source heat pumps in my old adobe use 3x more than we generate (which in turn is 3x more than we need during the summer). No (sane, residential) battery system can handle this.

Which mostly goes to show the value and necessity for serious insulation and air-sealing, which this house does not have. Nevertheless, the point about batteries remains.