xkcd

I think you may be mixing up Project Orion (let's chuck bombs out of the back to make us go zoom) with NERVA (a nuclear thermal rocket engine where the heat from chemical reactions is replaced with heat from a nuclear reactor to generate gas expansion out of a nozzle). Something like NERVA is actually a great idea. Let me tell you why!

• It's completely clean (unlike Orion and fission-fragment rockets)

  • the reactor and fuel never touch, the fuel goes through a heat exchanger and is not radioactive

• it provides extremely high efficiency

  • chemical rockets top out at ~400-500 isp in vacuum
  • NERVA tests in 1978 gave a vacuum isp of 841
  • ion thrusters like NEXT has an isp of 4170

• it provides lots of thrust

  • NERVA had 246kN of thrust
  • NEXT (which was used on the DART mission) is 237 millinewtons
  • That's 6 orders of magnitude more thrust!

• No oxidizer is needed

  • All you need is reaction mass, just like ion thrusters

For automated probes, the extreme efficiency and low thrust of ion thrusters makes perfect sense. If we ever want to send squishy humans further afield, we need something with more thrust so we can have shorter transit times (radiation is a bastard). Musk is supposedly going to Mars with Starship, and the Raptor engine is a marvel of engineering. I don't like the man and I'm not confident that he'll actually follow through with his plan, but the engineers at SpaceX are doing some crazy shit that might make it happen.

Just think though, if the engine was literally twice as efficient and they didn't need to lug around a tank of oxidizer, how much time could they shave off their transit? How much more could they send to Mars? Plus, they could potentially reduce the number of big-ass rockets they have to launch from Earth to refuel. If you can ISRU methane, then I imagine you could probably get hydrogen.

There are problems that still need to be resolved (the first that comes to mind is how to deal with cryogenic hydrogen boiling off), but like, the US had a nuclear thermal engine in the 70s. It was approved for use in space, but congress cut funding after the space race concluded so it never flew.

I'm happy to see that NASA is once again researching nuclear thermal rockets. Maybe we'll get somewhere this time.

Don't forget the mass of whatever ablates from your shield!