Is there a not-obvious reason we don’t have these yet?
The radiation shielding would be too heavy, the steam equipment would be too heavy, and every plane crash would be an environmental disaster.
Three-eyed pigeons.
In addition, maintaining a fission reactor onboard an aircraft would be prohibitively expensive for what it actually does. Here is a relatively succinct summary of the Nuclear Energy Propulsion of Aircraft and Aircraft Nuclear Propulsion programs in the United States.
Stranger
The US experimented with an airborne nuclear reactor (it didn’t power the plane, though):
The idea never got too far - too heavy as I recall.
To get an idea of some of the challenges, read up on Project Pluto, may favorite “Mad Scientist” weapon of all time - this was an unmanned flying nuclear ramjet. Keep in mind that you didn’t have to shield a crew, deal with landing gear, make it safe to be within a country mile of the flightpath, etc. Even then it was evidently quite an engineering feat. Now add in those other constraints and you can start to see how difficult it would be.
Also see the Supersonic Low Altitude Missile (SLAM), also known as “The Flying Crobar”.
*Apart from the thermonuclear warheads, SLAM itself was also a very formidable weapon. The sonic boom of a 25+ m long vehicle flying at Mach 3+ at 300 m altitude would cause severe destruction in non-hardened structures on the ground. Additionally, the nuclear ramjet continuously left a trail of highly radioactive dust, which would seriously contaminate the area below the missile. Finally, when the SLAM eventually crashed itself at the end of the mission, it would leave a wreckage of a very hot and radioactive (“dirty”) nuclear reactor. *
One of the major concerns was where you could base this thing without doing significant damage to your own people as it flies out. Eeek!
Stranger
The OP asked for a not-obvious reason. So far all the responses seem fairly obvious.
A not-obvious reason would be, a conspiracy of meteorologists, suppressing promising research in nuclear technology, so they can continue getting grants to study AGW. That is not obvious at all.
Nor is it rational.
Moving right along…
two X-39 atomic aircraft engines are on display at the Experimental Breeder Reactor I site in Idaho:
The shielding problem was insurmountable: you simply couldn’t build a reactor that could put out enough power to lift the weight of shielding necessary for that level of output, at least not with a crew aboard.
Another problem was the actual power/weight ratio of the reactor itself: in order to have a power output equivalent to a conventional engine burning ordinary jet fuel, the reactor had to be white-hot, on the knife edge of either melting itself or exploding like a dirty bomb. Note that in a conventional engine (already almost as hot as the current state of the art in engineering can cope with), the fuel/air mixture heats itself internally from combustion; a reactor by definition has to be hotter than the airflow it’s heating- a LOT hotter to have a useful power ratio.
The main purpose of a nuclear powered aircraft would have been unlimited range and the ability to remain aloft for long periods, away from being destroyed on the ground by a preemptive strike. The range problem was solved by the perfection of in-flight refueling, and ballistic-missile submarines became the chief guarantee of having a survivable nuclear arsenal.
I recall seeing a show that pointed out that the circulating liquid directly heated by the reactor became itself radioactive. So that required a second circuit of liquid - the first circuit in direct contact with the reactor heats the second circuit which is now relatively safe to exhaust as it is used to turn turbines, props, whatever. This results in huge efficiency losses and huge weight gains. Of course if you want to cut out the second circuit and vent the material directly in contact with the reactor onto the turbines, etc, go right ahead. But you will leave a radioactive cloud behind you and likely kill the aircrew and groundcrew as well.