But you also concede that you can use LNG from time to time. Which we can later switch to H2 or NH3.
Right now, all the natural gas power plants in the US produce about 12% of the total (gross) emissions. If we use these plants only when there's not enough electricity from solar, wind, hydro and nuclear, we'll reduce their emissions by a factor of 10.
What is the point in building thousands of reservoirs then? To reduce that 1% to 0%. Which we'd reduce anyway once H2 or NH3 become cheap and abundant enough?
By the way, the EIA made a handy comparison table for various power plants [1].
A "combustion turbine - industrial frame" is by far the plant with the cheapest capital cost, only $785/kW. Conventional hydro is listed at $3083/kw, with a fine print footnote that this cost is the least expensive plant that could be built in the Northeast (where the geography permits).
So, the cheapest possible conventional hydro is 4 times more expensive than an brand new natural gas power plant. My point is, we don't need a brand new one. We can just keep existing ones (and we don't even need to keep them all).
[1] https://www.eia.gov/outlooks/aeo/assumptions/pdf/table_8.2.p...
Concluding that we'd only need 2% of the current emissions from this is a bit misleading. The overwhelming majority of emissions currently don't come from electricity and the only way to replace many of them is via electrifying them.
Some can be turned into opportunistic loads, but there will still be a major need for 4-100 hour storage in addition to the seasonal storage (which will be largely achieved via hydrogen or ammonia).
Off river PHES seems to currently be cheaper than other storage, but chemical batteries have a lot of other advantages and may become cheaper.
It also has at least one advantage over conventional hydro in that sites can have a lot more head. This allows the power room to be a lot smaller, and there are many brown field sites where one or both reservoirs are mostly complete (which may make it cheaper in spite of needing two reservoirs).
It's hardly 'the only game in town' though, and it's unclear whether the gap between 'batteries have much lower cost per watt' and 'ammonia has much lower cost per joule in storage' is big eough that 'a hole has zero long run cost' the marginal efficiency gain over electrolysis is worth it.
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?
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.
For tertiary, occasional use, efficiency doesn't matter much, and other considerations dominate. Gas and steam turbines need expensive periodic maintenance after operating for some period, so you avoid running them too much. Fuel costs money, too. (Unless you synthesized it yourself; but what you burn you cannot sell.)
Transmission lines complicate choices further, in large part because they go both ways, and must be scheduled to maximize usage because they cost a lot to build. The power they carry might be free at the source.
Pumped storage round-trip efficiency is not, in fact, 25%, but routinely above 70%.
Nobody pumps water up just 10 meters. It is, instead, pumped (say) a thousand meters up to a reservoir commonly 10 meters deep. A 10m-deep reservoir needs only an cheap earthen dike. A dike is hardly a "megaproject", even if km long. Dikes are low tech.
The energy is extracted at the bottom end of a penstock. Each ton of water in a reservoir 1000m up stores 10MJ. One just 100x100x10 meters thus holds 100,000 tons, 1000 GJ, >270 MWh, 6 hours at ~40 MW.
Nobody needs 30 days' storage. If your hydro storage runs low, and local fuel tankage looks like it might, too, you order out for LNG or, soon, NH3 or LH2 from solar farms in the tropics.
Few would need or want a 1km x 1km reservoir. Smaller ones distributed where the power is needed are more useful.
An underground cavity, where it exists, can be used instead of a hilltop reservoir, or with one.
Burning NG once in a while is no big deal, but NH3 will be cheaper in the near future.