You're absolutely right that traditional electricity can't be stored. You can charge batteries with direct current electricity, but that's more for off-the-grid homes. That way they can be self-contained. The idea of enhancing the grid by diversifying your source of generation is that you actually have a stronger grid by having generation throughout different parts of the grid.
Traditionally, we've put things in large centralized plants and then distribute out, with the inherent line losses, etc. The idea that we could ever see so many net-zero homes that would oversupply the grid is probably a far-reaching problem that we'll never get to, because as we add these homes, we add many other energy-consuming industries to take up the slack. So there will always be a lag, I believe.
From a utility standpoint, there are many questions about ensuring the safety of the grid, so if there is a problem in the grid you would ensure that producers aren't feeding the grid while someone is actually up the pole trying to fix the grid—that sort of thing. Those are more logistical questions, but that's quite doable with building in the logic with the interconnects to the grid.