Look at the countries that produce all or nearly all their electricity from renewables. It's dominated by hydroelectricity: https://en.wikipedia.org/wiki/List_of_countries_by_renewable...
And since it's a well understood problem we can just build it everywhere, in arbitrary quantities.
And you need a reservoir down below to receive the water as it passes through turbines otherwise you're waiting for rainfall to fill that upper reservoir up naturally.
The geographic conditions to make pumped hydro are far more constrained than you seem to think. Most water reservoirs for municipal water supplies don't have the elevation drop to be used for generation and they don't have the lower reservoir to capture and feed water back into the upper reservoir.
I feel like we still have some problems with dam building, because they keep failing. We struggle to get the building material (in particular, sand). Concrete is pretty awful in terms of CO2. Dams of all sizes cause problematic changes to the rivers they're on, and block flows of fish and other animals. Smaller low head weirs and dams kill humans.
Lots of time, money, and effort is going into removing smaller dams and low head weirs.
So they'll buy your night time energy for the few hours a day when the wind farm they contracted with for less than your O&M costs isn't producing. Still doesn't help the nuclear operator pay the bills for the other 22 hours. Unless you're suggesting we ban people from supplying their own energy or making contracts with fully privately funded wind generators? Sounds pretty un-free to me.
> Why don't we just use hydroelectricity for all of our power needs? Ditch nuclear, and ditch solar and wind. Just build dams. Problem solved
You cited a need to store energy for moving water from a reservoir to where it is needed. Storing the amount of water you need to store but raise it up a little bit is a fairly well understood problem.