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Batteries, mass of batteries.
Not feasible.
It's barely feasible to use pumped storage for solar to match the daily demand curve in some small areas. Grid scale storage cannot be feasibly scaled to serve our current overnight power needs. But the daily demand curve isn't the problem.
The real problem is the seasonal variation.
For solar to be effective, it needs to be able to meet our winter demand with our winter sunlight. 9 hours of low-angle sunlight under largely overcast conditions. That means we need a lot of solar panels, to get sufficient power from these suboptimal conditions.
Now, take that same number of solar panels, and give them the 15 hours of high-angle sunlight under largely clear skies that we have during the summer. When we do this, we have so much power pushed on to the grid that the price of electricity actually goes negative. They literally have to pay people to take it.
There isn't enough lithium in the world to make the batteries we would need to balance seasonal variation. There isn't enough land on the planet to support pumped storage facilities that could balance seasonal variation.
We need demand shaping to make solar feasible as our primary energy source, which means driving our heaviest loads to daytime, away from the dark. (This is the exact opposite of what we need to do for nuclear, coal, and other baseload generation.)
We also need 3-season industries that can soak up excess production in spring, summer, and autumn, while going offline and shedding their loads during winter.