> When prices go down or even negative, a CHP or windmill is shut down in minutes.
Negative prices are a symptom that the (day ahead) market is not the real game being played. CfD, production subsidies and renewable credits are the order of the day.
> The nuclear plant ... will go below cost price
> its fuel is expensive as hell
The fuel is cheap. https://www.iea.org/reports/projected-costs-of-generating-el... estimates 9.33 USD/MWh (2018 prices) for fuel.
> in France some plants were shut down because rivers dried up too much and they'd be heating up the remaining "trickle" too much with these plants.
https://www.politico.eu/article/when-the-water-runs-dry-why-...
The Bugey plant is also the main reason France must ask the Swiss to let more water through the Seujet Dam. While most of the water is released back into the river, the reactors need a constant, cool flow — and climate change isn’t only making the Rhône’s water scarcer, but also warmer.
> in France some plants were shut down because rivers dried up too much and they'd be heating up the remaining "trickle" too much with these plants
Looking at https://www.euronews.com/green/2023/07/13/frances-nuclear-po... it appears power was reduced due to river temperatures, not river levels. That makes it more a regulatory issue, and probably one solvable with more hardware (extra cooling towers or greater extraction).
One might also ask whether it is worth EDF investing to get the extra few percent total output across the year; the solar peaks during hot weather will tend to reduce the price of electricity, so why not just schedule maintenance at that time of year. Thus PV creates a problem that it partially solves.