If solar were free, but we still needed to pay for battery storage, how would it then compare in cost to fuel-based alternatives (fossil fuel, nuclear etc)?
Would need $20/KWh battery storage to be competitive with nuclear for baseload according to
https://www.cell.com/joule/fulltext/S2542-4351(19)30300-9
At the moment, we're at about $800/KWh.
Aren't car battery packs under $100/KWh? Is there some other factor which drives up the price for grid level storage?
The factor that drives up price for grid level storage is scale. Only ~300 GWh worth of batteries is produced globally each year. The world uses 2.5 TWh of electricity each hour. If anyone tries to install battery storage at a significant scale, demand will vastly outstrip supply and drive prices up.