The more interesting climate advantage of nuclear power is it can be used directly in manufacturing, for example in creating steel (which represents 8% of GHG emissions). You can't make steel with electricity - the current strategy involves essentially setting a bunch of oil on fire on top of the requisite components (you can tell I'm not actually an industrial engineer, but steel generation is very not green).

However, you could harness the heat from a nuclear plant directly (instead of using it to create steam and drive turbines) to create steel. This has been discussed for decades[1], but modern improvements in nuclear technology could make it a reality

[1]: https://inis.iaea.org/search/search.aspx?orig_q=RN:8341064