Right now, household batteries are being installed by those that can afford them (and the prices dropping). They are enough to handle overnight load. And electric vehicles are becoming popular, usually with double or more capacity, which will replace the household batteries. The uptake is high and will only get higher because it saves people money. Even people who can't afford a household batteries themselves will be able to get one installed, as the cost saving will allow someone else to profit. So grid batteries are easily able to provide sustained load to the grid, by simply pricing power from the batteries higher than power direct from the generator. Household batteries kick in because it saves people money, and turns out you need very little grid storage at all to handle overnight load. The trick is handling black swan events, such as extended periods without wind or ash/dust blocking sun, across the entire grid area (usually solved by making the grid bigger, such as connecting to neighboring countries).

Any civilisation that can produce a 60kWh battery or three per residence for gigantic EVs can trivially produce a 30kWh battery for overnight storage. Prices are at around $150/kWh at the cell level and assembly costs are plummeting, there's no real reason to think 12 hour Sodium-ion, Iron flow or ZnBR storage won't be available for prices close to the PV required to drive it daily.

It won't be needed because renewables can provide 70-95% of hours just by adding dispatchable loads even without adding more PHES or CSP, but it's not because batteries will be exorbitant compared to non-renewable generation options.