You have to pay off the initial construction costs. Throwing away half the energy you generate means that you're wasting the large up-front costs.

Right. If we build nuclear plants to fulfill peak energy demand (which coincides with a lack of energy production from solar) then there's not reason not to just run the nuclear plants 24/7 and skip building solar altogether. This is why nuclear power and intermittent sources end up being a dichotomy in practice.

Solar does provide a good way to mitigate carbon emissions in the meantime, even if it's role in a fully decarbonized economy is dubious. It's fast to build and makes a good complement for gas plants. Turn off the gas when the solar cells are collecting, and you can save a good deal of emissions.

Solar also has niche use cases that make sense even with nuclear power. Rooftop solar is a good way to offset air conditioning energy use. In this case, the solar energy collected by the panels are intrinsically connected to the power demand of the air conditioning unit. Plus the energy production and energy demand are co-located.

You're missing the point, which is that if you don't use a nuclear plant to 100% capacity (or run at 100% capacity and throw away most of the energy), you end up paying more for every Joule you actually use.

How much would it cost to build nuclear power generation capacity to meet peak demand, vs. building a grid with renewables, long-term transmission and storage? The levelized cost of solar and wind power is way below that of nuclear power (and that difference will become much larger if you're only fully utilizing nuclear power during the daily peak demand), so the question is how much storage and transmission add for renewables.

One of the interesting possibilities for new nuclear plants is on-site thermal storage. Store heat from the reactor in a heat sink when solar is generating, use the heat to generate power when it isn't. That handles the daily load variation and lets you trade half the required nuclear capacity for cheap solar.

It also means you have more turbines on site than the reactor needs on its own, so you can add a furnace burning whatever you like (hydrogen, biofuels, synthetic methane), and that handles the days when renewable output is below average.

+1 I wish this were further up. Reliable power is always better than unreliable power. "Base load" is a misleading concept because people conflate supply-side and demand-side fluctuations, which are generally unrelated except in "niche use cases" like you mention. You always need some sort of storage or on-demand generation to deal with demand fluctuations. With wind/solar, you need extra storage to smooth out supply fluctuations.