If every household did this we would have massive problems. We would still need a base load amount in the winter, and in the summer there would be an over abundance. The price of electricity would swing between essentially free in the summer to higher than normal in the winter, because the cost of operating base grid power would be about same but they would need to cover all operating costs during the winter.
Utilities should charge a separate connection fee and per-kWh rate if that's what matches the economic reality of their business. I don't see the summer abundance as an issue. It means we get to shut off the fossil fuels 8 months out of the year. The remaining 4 months, everyone pays a little more per kWh, averaging out to the same cost over a full year. What's not to like?