This was one of the first uses of nuclear technology patented after the Manhattan Project. Up until he died, Richard Feynman held the patent on the nuclear airplane and locomotive. When the Air Force was involved in their chicanery with this idea, Feynman actually went and demanded payment for using his idea.
As noted in the links posted above, the idea ever really got off the ground, though.
More than the safety aspect, I think the engineering is the gotcha, here. Weight is a driving factor in any aircraft design, so we use exotic materials and safety factors that would be considered obscenely small to other engineering disciplines. I cringe at the thought of a reactor made of plastic composite, or with a 1.01 safety factor.
