The biggest issue with batteries is that they are not a prime source.

In a healthy grid with a diverse generation mix, batteries are almost certainly the perfect option for peak demand handling. The problem is that many grids are not healthy or do not have very diverse generation mixes.

You are effectively borrowing from yesterday (or last hour) to pay for today with batteries. Which is amazing, until it isn't. The Texas winter crisis comes to mind as an example where batteries would be regarded with intense derision. I think the current capacity market accreditation process is massively underrepresenting the tail risk of a black swan event. Four hours of battery storage should not be in the same room as a gas turbine when we are talking about capacity and multi-day emergencies.