Let's say you want to reduce emissions by the equivalent of a 1GW natural gas power station.
Option 1: Build enough solar and wind to replace the electricity generated by the power station; in fact overbuild by let's say 30%. You can afford that because solar and wind are cheap. And then build pumped storage to be able to add an extra 300 MW for a few weeks, when you need that. Decommission the natural gas power station.
Option 2: Don't build the pumped hydro. Build instead twice as much solar and wind as in Option 1 above (for less money than in Option 1, because pumped storage is so expensive compared to solar and wind). When they can't provide 2 GW of electricity, fire up on natural gas power station to make up the deficit. Decommission one natural gas and keep one in partial use. Achieve more emissions reductions for less money.
My point is that pumped hydro is hardly being built, but battery storage is growing very fast even at much higher costs (due to the other advantages). Step zero is, as always, build wind and solar but once you reach step one (and some places have) pumped hydro is hardly 'the only game in town', and it's not even obvious if it will remain a good option even if you have an excellent site.
Battery storage being built today is, correctly, almost all for shifting afternoon collection to evening usage, where batteries are best suited by their unlimited charge and discharge wattage, and their high cost per MWh stored matters least.
For storage beyond 4 hours, other considerations become important, particularly cost per MWh stored. You still need to extract plenty of wattage, but charge rate matters less. So, you need big or many turbines, but pumps can be slower. And, of course, retrofitting the many existing reservoirs is cheapest, so you do that before building anew.
Fuel storage similarly takes advantage of existing combined-cycle turbines, which are being adapted to burn a gradually increasing fraction of hydrogen. It remains to be seen whether they can be made to burn ammonia directly, or if the ammonia must first release its hydrogen. Stored fuel has the great advantage that it can be shipped, bought, and sold.
Option 1: Build enough solar and wind to replace the electricity generated by the power station; in fact overbuild by let's say 30%. You can afford that because solar and wind are cheap. And then build pumped storage to be able to add an extra 300 MW for a few weeks, when you need that. Decommission the natural gas power station.
Option 2: Don't build the pumped hydro. Build instead twice as much solar and wind as in Option 1 above (for less money than in Option 1, because pumped storage is so expensive compared to solar and wind). When they can't provide 2 GW of electricity, fire up on natural gas power station to make up the deficit. Decommission one natural gas and keep one in partial use. Achieve more emissions reductions for less money.
Which option do you choose?