Well, if we had cleaner nuclear power - say, aneutronic fusion - that wouldn't have the radiation risk and could result in far lower shielding and therefore weight penalties, then yes, this is not only possible, my guess is it becomes beneficial from a pollution/greenhouse gas emissions standpoint.
But look at what's standing in the way: A theoretical technology that's not been engineered in any practical manner yet. I might as well be saying "if we had magic", the only difference is that aneutronic fusion is a known physical process that humankind has so far not yet been able to make work for us. Yes, I might as well be invoking magic since both are similarly unreachable right now, despite the real-world foundation behind one of them.
Fission reactors, I fear, would just require too much shielding to be practical. And then there's the radiation issue. But yes, I've actually had very similar thoughts myself, to be honest: How would we make nuclear power work for us vis-à-vis air travel? The devil is in the practical details. And unfortunately mankind's state of technology is not in a place where nuclear aircraft propulsion makes any practical sense.