especially in comparison to something that is cheap and ubiquitous

In some countries nuclear is cheap and ubiquitous. The key is simple standardization.

In France for instance, nuclear accounts for about 70% of their power. They operate 57 nuclear reactors, all of which are one of 4 reactor designs. By having standardized designs these reactors are cheaper to maintain, parts and equipment are more available. The engineers that run the facilities are more familiar with every aspect of the plant, operating procedures are better understood. It's easier to find qualified engineers and technicians. Accidents are uncommon (I believe they've never had any kind of major accident).

The price French households pay for power is comparable to what we pay in the US and they generate significantly less CO2 per capita. They also have less reliance on oil states.

We could have that too if we were motivated to make it happen.

Nuttery?

Every dollar spent at NASA has returned so much more. They develop things for space travel that have uses far beyond space. We wouldn't even have satellites and GPS if we didn't venture into space.

Space has a lot for us to explore and a ton of resources we can use. Why strip mine the Earth when we could just take it from the asteroid belt?

You really need to disconnect space exploration from the likes of Musk or Bezos. We've been advancing humanity through space exploration before those two assholes were born

Nuclear power is a very important technology for space vehicles, probes and bases. There's proven potential for greatly improved propulsion systems as well.

You can't just hear the word space and declare it "nuttery", that's just ignoring whole industries and areas of active research and engineering.