> The per-unit cost of nuclear power plants is extremely high, making it hard to get economies of scale in building more of them.

I disagree. building big infrastructure projects always scales well. As stated by the project managers at Hinkley Point C (the most expensive nuclear reactor ever) they estimate that build times and cost will be significantly reduced for the second reactor due to the knowledge and expertise baked into the workforce. Frances nuclear revolution during the 1972 oil crisis also shows the same thing with construction cost getting lower the more reactors built.

There are other reactor designs that do not use uranium that have been tested and hypothesized.