Batteries are very expensive for long term storage. Batteries need to be cycled frequently in order to earn enough money to pay off their rather high cost.
This isn't a unique property of batteries. Any storage system faces that: batteries, pumped hydro, or your proposal of melting salt and storing it in a cave. They all need to amortize their construction cost over the cycles they'll be used.
What we're seeing right now is that for daytime generation plus overnight storage, CSP and PV+batteries are pretty similar cost. If you increase the storage component of each, the price of each increases because they're bigger, but you don't increase the amount of electricity coming out, so the price per kWh goes up for *both* systems.
Let's separate power and energy. Power is watts. Energy is watt-hours. Power tells us how "strong" the flow is while energy tells us how long that power flow can be maintained.
If you have a 1 kW battery that has a capacity of 1 kWh then you can power something that takes 1 kW for one hour.
If you have a 1 kW pump-up hydro storage facility (PuHS) that has a capacity of 1 MWh then you can power the same device for 1,000 hours.
To get the same storage as a 1 MWh PuHS you'd need to purchase 1,000 1 kWh batteries. At this point in time, and probably forever, it will be cheaper to dig a larger reservoir for PuHS or use a big cavern and lots of cheap salt, or build large storage tanks for flow batteries than to manufacture chemical batteries.
Batteries might get cheaper than other storage technologies for single day storage but mass storage is likely to continue to be the long term storage solution in terms of cost.
Let me try to explain what I think is the best solution based on what we have right now. With the assumption that batteries will become the cheapest "one day" technology.
Assume that during "normal" wind/solar days we produce more electricity /energy that we need and half the time we produce less. The task is to shift the over production to the under production hours. But there are stretches of one to ten or more days when we produce less than what we need.
So we use a combination of about half batteries and half 'deep storage' like PuHS on normal days. That way the batteries get their frequent cycling which keeps their cost low. And PuHS gets to make money every day which pays for its pumps and turbines. Each store energy half the time and use that energy to supply power half the time.
Now we hit a low supply day. There's no surplus to store, everything from a wind farm or solar panel gets used. We need deep storage.
So we run the PuHS 24 hours a day until the low supply is over - until the Sun and wind input picks back up.
When demand is less than what reduced output wind and solar can cover the extra power coming out of the PuHS charges batteries. When demand is greater than what wind/solar/PuHS can cover the batteries come into play.
As long as there is adequate water in the upper reservoir of the PuHS (or chemicals in the flow battery tank or molten salts in the chamber) we can keep the grid functioning with no disruption.