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If you were to turn off the coal supply, wouldn't the boiler quickly lose heat, particularly since we're extracting energy from it?

Even if it takes an hour to cool down, since daily and weekly patterns are generally known, can't they reduce or stop the coal supply an hour in advance?

In a world with more renewable energy, perhaps coal plants can be designed with smaller boilers, to strike a different tradeoff?

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Coal plants are not designed to be constantly started and stopped. For one, constantly cooling and reheating the equipment would damage the metal.

That may be true historically, but is it not possible to design them in the future with that goal in mind?

You are burning a lot of coal for no energy if you spend an hour a day starting and an hour a day stopping a plant.

I assume "less energy", not "no energy", but in any case, what better alternative would you suggest in a grid with significant amounts of intermittent sources, like 70%?

Pumped hydro or battery storage are one possibility. Smart pricing to industry who can throttle back usage if demand outstrips supply is another.

Or some combo of both of them.

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