only natural gas plants can do this. a coal plant cannot spin up just for the night and turn back off when the sun comes up - it's incredibly inefficient and probably causes more premature wear/tear too.
The big issue is what's called "ramp rate" - how fast can output power be increased or decreased? This tends to be around 1% to 3% of capacity per minute. See Figure B-2 in [1], which is a detailed discussion of how to improve your coal-fired power plant's ramp rate.
Natural gas plants have much higher ramp rates, and for batteries, it's under a second. Nuclear plants can be ramped up and down, slowly, but since it's all capital cost, cutting output raises the price of the power.
"Increased rates of component life consumption due to thermal fatigue, mechanical fatigue and wear caused by differential thermal expansion comprise the bulking of cycling (costs)," according to the International Energy Agency's Coal Industry Advisory Board.
"Every time a power plant is turned on and off, the boiler, steam lines, turbine and auxiliary components go through unavoidably large thermal and pressure stresses," the National Renewable Energy Laboratory (NREL) wrote in a report on cycling costs published in April 2012.
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https://www.reuters.com/article/business/energy/to-survive-c...
Batteries are coming, and will solve it, but it will still take time for them to be come cheap enough.
Only once we have ~7 days of storage (~100 GWh of storage) will we be able to get rid of the last fossil plants.