There was an enormous amount of fooferall around nuclear-powered satellites being flown out of Cape Canaveral, and the potential fallout on the general public if a rocket were to fail with such a payload. Then people just stopped talking about it, and we launch nuclear shit all the time. I still think we should package our nuke waste into rockets and shoot them at the Sun. But yeah... those rockets have to fly over someone's house on their way out of the atmosphere...
Why yes! Yes there are. (1) They're about as inefficient a reactor structure as you could ask for. (2) They slowly turn from nuclear fuel to nuclear waste before your eyes. (3) The more power they put out the more radioactive they are. Compare and contrast - the RTGs on Voyagers 1 and 2 weigh 38 kilos and put out 157W. Good thing it's got three; that's 120 kilos of generator (13 kilos of plutonium - about 1/5th of the bomb we dropped on Hiroshima) for 460W. On the other hand, the solar panels on Juno weigh in at 340 kilos but in earth orbit they put out 12,000 watts. Tweaked to work out there around Jupiter they still put out about 500W.
It's fair to say there are no nuclear airplanes because a fissile pile and its associated care and feeding are detrimental to power-to-weight. It wasn't exactly a new strategic location. SAC has had a presence in Greenland since like Midway and we had a vested interest in getting Denmark to leave us the fuck alone with their tedious nascent environmentalism. More than that, the B-36 (the front-line strategic bomber of the "atomic planes" era) had a conventional tricycle landing gear arrangement that necessitated hardening runways to put up with its loads; it would literally dig furrows in non-fortified strips. There were only six or seven air bases in the world they could operate out of. So this whole "let's just make them nuclear so we don't have to deal with this shit" approach was more than "nuclear nuclear rah rah rah". Jets got more efficient and bombs got more efficient and before too long, it made no goddamn sense to use nukes for anything other than blowing shit up. The first flights of the B-36 and B-52 are separated by a mere six years; doctrine went from "make it bigger" to "make it cheaper" because we'd kind of fished the limit for "things that go into the sky."
At one point, the United States offered $100 million in gold to purchase Greenland from Denmark and gain a new strategic location for bases. In the end, Denmark decided to keep Greenland, but the proposal illustrates the lengths the United States had to go to compensate for its planes’ limited range. A nuclear-powered airplane could avoid all of these issues.
Charles Stross wrote a sort of lovecraftian alternate history spy thriller short story (novelette? Novella? Not sure what the word is in English) called A Colder War where both nuclear-powered aircraft and Project Pluto were built. I highly recommend checking it out, it's definitely one of my favorite short stories ever (although the online version I linked to is missing some stuff that was in the version published in eg. one of the The Year's Best Science Fiction collections by Dozois)