You can (and this is being done in practice) regulate the power output instead of turning it off completely and then turning it on again, doing it your way would be extremely detrimental to the power plant's life due to thermal stress. It's also the case that different coal plants have different capabilities so when you claim it takes a around week to turn off a plant, you should provide some more information about the plant (type) you're talking about.
Coal plants for load following end up around 20-40%, nowhere near your 80% number. They have to, because the energy grid demands that they're capable of doing this because it's just not economical to run them at 80% when there is such variability.