I think eventually closed cycle nuclear propulsion would be used to exit from earth. A more advanced variation of nuclear thermal rocket with higher specific impulse and still having enough thrust would be more efficient, requiring less propellant than chemical rockets. Since its closed cycle the exhaust won't be radioactive waste.

The issue isn't with nuclear propulsion per say, but what happens if the launch sequence fail (wether its by chemical engine failure or otherwise) with a nuclear reactor (active or not).