Radiation is as big a problem on Mars as well. Unless we will live in ant farms (remember those?).
Graphite (aka pencil leads?) is not mechanically strong, is flammable, etc. That Chernobyl reactor was a graphite-based design. Putting the reactor inside a safe shell is very heavy and still no guarantee for crashes or uncontrolled reentries. Plutonium thermoelectric power packs have been used previously (ignoring above safety reservations). One is used in “The Martian.” Note: we are running out of plutonium!
The electrical energy generated by the reactor or power-pack still must produce thrust somehow. Inertial engines use Newton’s third law by shoving something out the back. So you still need something to shove out. More, heavier, faster → more thrust. Most efficient specific index is for ion propulsion, used to get to Pluto. Minute thrust over long, continuous time. Took ten years.