We don't have nuclear powered aircraft because the required shielding was too heavy. Both the US and the USSR tried in the 1950s and 1960s, but the only "successful" program was the Soviet Tu-95LAL which got around the problem by simply omitting most of the shielding, irradiating the crew.

Then the ICBM made the strategic bomber obsolete, and there was no incentive to sink any more money into nuclear-powered aircraft. Concern for safety had little to do with it, especially if you compare it to other occurrences at the time [1]. Now we can build autonomous vehicles that don't care about radiation and can make use of all that power, and that's exactly what Russia is doing.

0: https://en.wikipedia.org/wiki/Nuclear-powered_aircraft

1: https://en.wikipedia.org/wiki/List_of_military_nuclear_accid...