We still need storage solutions like this for long term storage, though, as batteries are mainly used for load shifting and short term arbitrage right now, at 6 hours of discharge and less.
They can essentially do this instantly, i.e., substantially sub-wavelength of your line frequency (a PWM of 10 kHz isn't even high for an inverter, and 100 kHz is well within what's feasible for large systems operating at a couple hundred volts; 10 kHz would equate a light-speed delay of 30km, 100 kHz of just 3km, which gets into the territory of relativistic w.r.t. medium voltage rings in cities).
The issue with solar is not the storage from day to night, but the storage from summer to winter.
Hydro systems and pumped storage look useful in this but the extent of summer winter variance is very specific to latitude and much of the planet isn't as badly affected. Wear transmission losses, buy power from lower lattitudes
Batteries output DC. They need an inverter to be connected to the grid. The inverter needs to choose a phase angle at which to output current and voltage, through something that looks suspiciously like a boost converter. This doesn't have to be quite the same phase as the line, it can "lead" or "lag" in an attempt to push the line phase angle back to what it's supposed to be.
Arguably batteries are ideal for the problem. However thermal storage systems like this one have good scaling to storage side of things: insulation is cheap, adding tanks is cheap. The basic turbine cost can supply wallplate stated power, the tankage gives duration and you can add as many tanks as you have room for.
Alongside simply supplying the energy, batteries are great for maintenance of supply frequency but I don't understand how they do reactive power. Turbine based systems do reactive power really well because of the rotational torque (I think) so represent a distinct role in electricity supply stability. (Its entirely possible batteries can do this too)
Finally, repurposing of steam turbine based generation sites means they have transmission systems, turbines on site and to hand: the capex component can be less.