Wouldn't you agree that we're much further along the learning curve for turbines than for large scale battery storage?

Presumably that would favor large scale battery storage, right? If large scale battery storage is already cost competitive with turbines and there is still more low-hanging fruit, then presumably battery costs will continue to fall faster than for turbines?

That said, I doubt the cost of either of these technologies is driven so much by the technologies themselves so much as it is our ability to manufacture and install large volumes of them at scale. Presumably it's easier to mass-manufacture batteries in a big factory and then ship them to the site than it is to construct each gas peaker plant on location, and moreover it's probably easier (i.e. cheaper) to scale up the manufacturing process for batteries than it is to scale up the construction process for peaker plants.