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.
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.
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."