> "Capacity firming" will be carried out by legacy gas turbines as they run less and less, and eventually by batteries

At least among the American TSOs, there are zero I know of that plan to do this. Do you have a source for one that does?

Trillions have already been spent on gas. That infrastructure will need to earn its return through the 2040s at the very least, and that precludes running them exclusively for firming. To the extent retrofits are being discussed, it’s as an add-on amidst full peaked functionality.

> Batteries are also much better than gas at frequency regulation

Limiting solar and wind by utility-scale battery capacity means scaling back EV adoption or solar and wind deployment. The math simply doesn’t work. (Again, in America. Without significantly raising rates. Not sure elsewhere.)

> it only takes a very small number of grid batteries to completely solve that problem

Frequency regulation is one component of firming. Batteries are good at some components, marginal at others. (As a system. Technologically, they're fine.)

Apart from de-industrialised grids, a batteries-only approach has been practically abandoned through the 2030s. It's why we're building so many turbines and abandoning nukes.