There's no technical need to do that, because someone who can always deliver electricity would be able to struck contracts with those that always need it, i.e. heavy industry, esp. aluminum and chemistry. The reason why downregulation was necessary in the 2000s and 2010s was regulation ("Einspeisevorrang"), not technology.
If someone takes it near the power plant, and all the infrastructure is there for it. You don't build a (large) nuclear power plant just for these customers though.
Generally, with a high amount of renewable but fluctuating supply, we have to get away from the base load model, towards a residual load model.
This is not true, since you still need to pay for capex and depreciation. The reason it appears to be free is not because its production doesn’t cost anything, but because at times of a glut there‘s just no one willing to pay much for it. Please make some good will effort to acknowledge the difference between cost and price.
Now, about your question, why people should buy „expensive“ nuclear power: for the same reason that people buy health insurance for: volatility increases risk, and you’re willing to pay an ongoing premium to reduce systemic risks. Over- and undersupply of electricity are risks for a lot of businesses and lots of them spend a lot of money on capex to avoid them, e.g. hospitals that have diesel generators. Generators are for a different failure mode (rare, longer duration outages), but for the high frequency, short time interruptions and/or price spikes caused by unbalanced generation volatility, contracts with a nuclear power company are similar; the capex is just shifted to the power company, and the customer might pay a premium during those times that other sources would deliver energy „for free“.
That said, this is not a black-and-white scenario. Of course we can benefit a lot from solar and wind. I’m not very positive about large scale batteries and lean more towards having flexible consumers, e.g. H2 production for the chemical industry. But right now, we don’t have the choice of nuclear vs. renewables, it’s (renewables + nuclear) vs. (renewables + turbines run with Russian gas or LNG from the US and Qatar). My choice here is clear, and it should not be muddied by the Russian propaganda of nuclear power clogging our electricity grids.
