It's not just a lack of storage capacity but grid stability. Grids need the inertia form large spinning turbines to balance the grid as supply and demand fluctuates. PV inverters, dont have any inertia, and they also track the grid frequency, so they dont resist any frequency deviation.
For this reason most grids need a mininum number of thermal plants to remain in production to provide inertia to the grid. There are now devices called synchronous condensors, which are basically enourmous flywheels connected to a motor/generator, that provide grid inertia for times of high renewables production. Google synchronous condensors.