> Also there's a limit to how much power you can draw through residential lines so regardless of whether or not batteries can deliver power on the same order of magnitude as a coal-fired plant, it's highly dubious that these specific batteries can do that.
These specific batteries, on the other ends of residential lines, indeed do push power back on the grid in aggregate enough to replace coal power plants. There's nothing special about a point generator on the grid versus the aggregate action of thousands of batteries on the other side of the distribution stations. In fact that's what's so amazing about batteries versus large thermal generators: thermal generators are large because if they get super inefficient when they're not large. Nobody is installing a small coal generator at their home to run daily, and even small diesel generators are hugely inefficient. But batteries are so useful that even accounting for the extra expense of large numbers of custom installs, they reduce grid demand enough to make a ton of financial.
And power is indeed the most important metric when it comes to the grid. It's how everything is run, how individual grid assets are dispatched, because power needs to be balanced at every moment. Somebody could throw an asset on the grid that only dispatched for 15 minutes (or whatever the minimum bid time is), and it would still be described primarily by power. Capacity decisions may be made in kW-month or whatever unit, but you can run a grid on a pure energy market without any capacity market at all, as ERCOT shows.