It's not quite as bad as that, since you don't consume fossil fuel resources when plants aren't running, but this is mostly a benefit for oil/gas plants, not coal (since the coal is likely useless without the power plant consumer anyway)
Depending on the type of power plant, it can take quite a while to spin up (or down) one of them and get them to optimal power production.
https://www.eia.gov/todayinenergy/detail.php?id=45956
If you shut down by day, it can take multiple hours for it to be able to provide full load... and multiple hours for it to shut down cleanly. During this time it is producing power at less than optimal rates and/or using the fossil fuels to keep the wheels spinning and in sync with the grid so that they don't have to go through a phase matching period.
(aside for coal - note that it takes more than 12 hours for a coal plant to get running from a cold start)
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Coal is a dead end anyway.