Take the simplest case and ignore CO2 and carbon tax for now. The base power stations have to be sufficient to supply the whole power grid when the wind doesn't blow, and the sun doesn't shine. Ok, so now imagine what happens if we simply remove all the solar panels and all the wind turbines. What happens? Nothing happens. The grid still works normally. In other words the cost of all those windmills, solar panels, their construction, their maintenance, etc, it is all extra cost that the consumer has to pay somehow.
So isn't the magic market supposed to fix all this? Why doesn't market dynamics take care of this? Because government regulation doesn't allow fixed power plants to charge a fixed yearly fee. If the government did allow this then the market would indeed price everything correctly.
Now if you add a carbon tax, having a number of windmills on the side does eventually become advantageous, but never compared to non-intermittent sources of renewable power like hydro or nuclear which could also charge this fixed yearly fee.
In the US, in most markets (except ERCOT/TX), it's the opposite of what you say. Government regulation _requires_ either the market operator or load serving entity to contract for capacity (as opposed to energy). PJM, which operates the largest market in the US, runs an annual auction for capacity. Incredibly, due in part to subsidies offered to the natural gas industry, existing nuclear power plants have not cleared in the auction. [0, 1]
[0] https://insidelines.pjm.com/pjm-successfully-clears-capacity...
[1] https://www.spglobal.com/marketintelligence/en/news-insights...
You are trying to simplify things too much. Unpicking a few factoids to make an argument. The advantage of this kind of energy market is that individual companies don't have to do that. Small developers don't need to worry about building backup for their solar panels. And nuclear power stations can take on a big risk. All bundles into the price.
But all this is specific to particular markets. No idea what is going on in the USA and as a European I assume it is probably a mess.
These kind of discussions always touch on a few of these points. But actually a well designed market absolutely can take these factors into account and price accordingly. You have strike prices to cover capital costs, capacity markets, bidding to reduce costs etc.
The low price of wind is just an acknowledgement that it is less valuable due to intermitancy. But you guarantee the rate regardless of the market because the low CO2 emissions are valuable.
Nuclear is expensive because it is more valuable due to low CO2 and low intermitancy. Give it a relatively high subsidised rate. It should be more expensive than wind.
Gas peakers are valuable because they can be turned on quickly. But they are dirty. So they charge a high rate but the rate is not guaranteed. The market avoids using them.
You could and maybe should replace all of this with a state run electricity company that makes all the decisions. That is really what people are arguing for rather than a particular type of generator. But in an energy market costs need to actually mean something more than a political point.