Maybe significantly cheaper though. Our generators often advantage of these events to gouge the grid by having 'unexpected maintenance' and restricting supply to force the market operator to buy their capacity at a much higher price. Having this battery act in a way that isn't profit motivated could actually change this market a lot.

What I gather from the (incomplete) data, indeed the backup plant would have fired up in about 6 seconds. Isn't it wasteful/inefficient/expensive though, to fire up a whole plant if just providing a few seconds of electricity from a battery is enough to bring a grid back to nominal frequency?

The reason the frequency dipped is because not enough generating power was online to supply the demand. In order to bring it back up to nominal frequency and keep it there, something had to keep supplying the extra power required for as long as it was being used.