The expensive bit about nuclear is not the fuel. It's making sure that the fuel stays where it is supposed to be. A different design might change the cost of that dramatically.
Not really. It's rather expensive (billions of dollars) to setup a nuclear plant in the first place, even before a single fuel rod shows up. Meanwhile solar is so cheap and easy that you can install panels on your roof yourself.
I agree that traditional nuclear makes little economic sense. But I disagree that this is inherent to nuclear power, because there might be a different reactor design that doesn't cost billions of dollars to set up. We just haven't found it yet.
One of the specific targets of the modular reactors that are now getting approval are these cost issues. If you build one reactor a year it will be big, bespoke, and incredibly overpriced. If you build a hundred modular reactors every year the cost will drop significantly.
