Yes, and no, maybe ;) the economic incentives are designed to always provide enough power and no more at the cheapest possible point for that time slot. The market (if free enough) searches for that point over time. One possible solution may be peaker plants (this was financially so in the burn fuel age) another maybe overbuilding (e.g. your home backup or off-site generator power that are sized at peak load/demand, not the actual demand). All constrained by what is physically possible on a grid.

Peaker plants gamble that there are going to be peaks (sure financially plan for but they are not guaranteed to make their profits).

In the peaker plant categories the storage options are different from the spin options because the incentives are slightly different. Specifically battery storage is not just a peak plant exercise it is a grid connection optimization exercise. Grid connections limit how much power one can sell from a generator. A battery system can be placed on the grid or between the grid and the generator. In the case of between grid and generator, it allows a generator to run at it's optimal speeds more often than not, and sell more because one can guarantee a wider range of output for a longer amount of time.

Some of the first battery storage systems were sold to gas peaker plants because it allowed them more time to react. i.e. idle at a more efficient level their gas turbines or even shut them off and start them on demand.