Renewable are all nice and good, but currently we're still building fossil fuel power plants all over the world. It would be better if we instead built nuclear plants. Expanding renewables and nuclear are not opposites of each other.
Is that a rhetorical question? Because night time usage largely relies on battery storage for which economies of scale are also reducing the cost in a similar predictable fashion.
However I will say there are newer solar panels that I've read about being tested which can theoretically produce power by moon light. Granted it won't be anywhere near the amount during the day but generating energy via solar at night time isn't entirely impossible it just won't be generating the same amount by orders of magnitude.
It would be cheaper to do any number of things(battery storage, Nuclear, world power grid) than to build out more solar capacity to capture the pitiful full moon light once a month.