However, it is much more expensive to build the capacity for batteries and you need to charge the batteries with excess power that’s available cheaply during surplus times.
The advantage of a peaker gas plant is you can build it big and shovel fuel into it that you just brought over from wherever. Many of them were built with the expectation that they would not face competition from batteries, so the economics of running them is getting bad. However they’re still important as a backup because you cannot depend reliably on the batteries being charged.
But this takes a while. And to heat things up faster, you simply burn a massive amount of fuel; which is costly. And until you generate steam, it's not actually generating any power whatsoever.
Any thermal plant has this overhead that makes starting them expensive and stopping them undesirable because the shorter you run them, the more inefficient they get. You amortize the startup cost over the runtime. The longer it runs, the better it gets.
A battery provides power within milliseconds and it can switch from charging to discharging on a moment's notice as well. That's why batteries are displacing gas plants as peaker plants in a lot of places.
It's my understanding that basically the entire point of gas power plants is that they are very cheap to stop and start (as opposed to e.g. coal or nuclear), at least, that's the case in the UK - are these plants different in the US?