Actually this is typically an issue for grid batteries.
Spinning generators can easily briefly go to 10x the rated current for a second or so to smooth out big anomalies.
Stationary batteries inverters can't do 10x current spikes ever - the max they can get to is more like 1.2x for a few seconds.
That means you end up needing a lot of batteries to provide the same spinning reserve as one regular power station.