Though with how SpaceX has been blowing up rockets left and right, probably a good idea to not have nuclear materials launching until that's been resolved entirely.
Boca Chica beach is a mess now, I can only imagine what new Fallout installment we'd get if South Texas became irradiated from a failed launch.
This isn't an issue at all: fission reactors aren't hazardous until after they first start up (go critical), which in the space electric-propulsion context means after (if) they've successfully launched, and are no longer in the vicinity of Earth.
At any rate, China is apparently[0] moving in this direction, regardless of what the US does.
[0] https://www.scmp.com/news/china/science/article/3255889/star... ("Starship rival: Chinese scientists build prototype engine for nuclear-powered spaceship to Mars" (2024)) (mirror: https://archive.is/sGUJr )
This is only true if the fission reactor's fuel isn't scattered over square kilometers after a launch failure.
But yeah, it's not dangerous like the P238 in a radioisotope thermal generator (RTG). To put off enough heat to power a spacecraft just through natural decay you need something ferociously radioactive.
We saw the hyperreactivity over Fukushima. I even know some very educated people who should know better like not wanting to eat any seafood caught in the Pacific.
It's bizarre to suggest that the same strategy would be used with nuclear materials onboard. Developing the "can not fail" rocket is the sort of thing NASA does well, and kind of highlights how we've squandered them.