That is not a problem, it is the incentive to have supplies available so they can be turned on.
I therefore wonder if the market couldn't be structured in a better way which would still ensure that the fossil backup generators are adequately compensated but smoothes the extra cost over the remaining cheap GWh. Something like a meditating party which is aware of the production costs and buys up the daily power and sells it on at an averaged price. There are probably good reasons why this wouldn't work, but I am too stupid to figure them out.
It's worth noting there are some demand response initiatives and the like that are approaching this from the other side - they will pay a user to not use power at particular times of high load. If you don't want to pay a premium on power, I suspect there will be providers happy to oblige, so long as you are willing to forgo the 100% service guarantee.
At this point there isn't really any part of the energy grid that governments do not subsidize. They subsidize companies that provide grid stability. They subsidize renewables that provide capacity. They subsidize the customer who buy energy. They subsidize the grid infrastructure that transports the energy. They subsidize the interconnection between countries that enables trade between countries. They subsidize the cleaning up and associated costs from pollution.