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I understand the contrary: nuclear power is extremely inflexible - not dispatchable, no demand response. You can't turn it off and on.

True, but solar doesn't have demand responsiveness either, it has sunlight responsiveness, which is not the same thing.
But unused capacity in nuclear overspeeds the turbines, you can't allow that to happen -- generation and frequency are both controlled by the same steam valve. Unused capacity in solar just sits there basking in the sun. The frequency is controlled by software in an inverter.

To make solar demand-responsive, you just build more of it. It's really that simple.

It's not about being dispatchable or not, it' about the volatility renewable generation and the problem this generates... and how other non-renewables need to be called by the TSO.
Renewables look at nuclear's inability to deal with the fluctuations and respond "That's a 'you' problem, not a 'me' problem."
Which is actually not true at all. Modern nuclear plants can be operated in load-following mode and reduce and increase their output by 10% and more within minutes.
The issue is not primarily technical, it's economic. Operate a nuclear plant at lower capacity factor and the economics becomes even more hopeless.
If the economics are impossible, how is it that France currently runs 70% of its grid on nuclear and has electricity costs substantially lower than the EU average?
We don't know how much those reactors cost to build then (it was mixed with the military nuclear program and the paperwork I understand does not exist to disentangle the spending). They are cheap now because they are not being charged for the cost of their construction. We do know that France cannot afford to replace them now; new reactors would be far out of the running economically.
So economically viable if the government subsidizes the construction. I would be happy for my tax money to go to a project that gets 70% of electricity generation off of carbon.
Subsidy doesn't change what the technology costs, it just changes how that cost is paid.

Subsidy can make sense, but not because shuffling euros around under walnut shells makes the cost disappear. The argument for subsidies is generally that it helps technologies move down experience curves. This improvement is a positive externality that a pure market would not necessarily reward. Unfortunately, nuclear (and nuclear in France) has been showing NEGATIVE experience effects.

That is not true the Cour des Comptes has extensive documentation for its cost, also nuclear LTO should be preferred, but replacement is economically possible.
The main issue is that the largest cost of a nuclear power plant is the capital investment to build it and staff to run it, which is fixed. In comparison fuel costs seem to hover at about 25%. Therefore you need to run your plant at about full power all day to have a chance to recoup the investment. With renewable, although intermittent, sources vastly undercutting nuclear energy on price many hours of the day this becomes an almost impossible calculation.

Based on this nuclear is an uniquely bad pairing together with renewables, and it will only get worse. Say you can make massive profits on average one hour per day, but that means all other methods of energy generation or storage can make the same, and still undercut you.

This isn't even factoring in that it is impossible to get insurance for a nuclear power plant.

Don't forget the costs for the waste which generations will have to take upon them.
A glass log at the ocean floor costs no one anything.
Could someone grab them, melt them, then make dirty bombs?
Of course! Anyone can grab something from the ocean floor (~3000m deep), especially something as easy to find as a lump of glass. Glass is also totally easy to melt on your kitchen stove and adding radioactive glass to the bomb you have lying around anyway, turns the bomb from a harmless firecracker into a totally menacing doomsday machine.

Yes, that's the first thing a terrorist would think of.

Seriously, dirty bombs are a red herring. It's the "bomb" part you should be worried about, not the "dirty" part.

Right. That makes it ideal for baseload. It can produce more than enough for regular loads. If necessary it can be augmented by solar and other power generation.
Let's be honest here--nuclear is not "ideal" for baseload, and it is indeed inflexible w.r.t. power output. What's actually ideal for baseload are fossil fuels. Unfortunately, those aren't going to be an option going forward, so we have to choose between a number of less-than-ideal options. I think it would be better to be realistic about the tradeoffs of those options than to try to argue that we actually aren't giving anything up.
Yes, you can. Most nuclear power plants are more dispatchable than most gas burners. Countries with lots of nuclear power plants (France) absolutely run them in a load following regime.

[Edit: And, as usual, downvotes rolling in for pointing out a verifiable fact. HN being HN, I guess.]

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