Thinking about the terrain, it would probably be relatively easy to setup a dam somewhere that acted as a battery, downstream is basically already a giant bowl... I suspect the tourist industry would complain though.
When nobody is looking at night, it pretty much stops.
Reducing water flow helps to preserve the falls too. The water has substantially changed their shape, even over a time period of 2-300 years: https://www.marriottonthefalls.com/blog/2015/02/06/rate-eros...
During the Post-Great Big Blackout period, the Falls power generation ran with night-time levels of diversion during the day-time. The tourist boats that go near the falls got furloughed.
https://en.wikipedia.org/wiki/Robert_Moses_Niagara_Power_Pla...
Evaporation is a real concern if you start talking about storing months of energy.
However, storing months of power is silly, you are much better off with extra ~6c/kWh wind/solar that you use 1/2 the year than trying to store ~6kWh energy for six months.
Renewable are the new base load power becase they are Cheap and you don’t gain from not using that energy. They still need peaking power or storage to follow the demand curve.
PS: Say it three times fast ‘base load power is a downside.’
But insane ideas are some of the best ones to explore further. In it might be something practical.
If you're willing to look outside the US, a wild but interesting mega project might be to try to do the same thing with the South Aral Sea. Pump water all the way from the Caspian. The North Aral is cut off by a dam/dyke and the south Aral barely exists anymore, causing major economic harm. Fill it with salt water and salt water fish to revive the fishing economy while using it as a giant battery.