> That is what fallout largely is.

Most of what you've said is right, but this part is not. The most radioactive parts of fallout are fission products, the split "halves" of atoms reacted during the nuclear fission part of the explosion. The reason surface bursts are more dangerous from fallout is not because the dirt itself became neutron activated, but because the fission products mix into the dirt, which makes them fall out of the cloud much sooner than they would otherwise. The mushroom cloud from an air burst is still highly radioactive, it just doesn't (usually) send its products back to the ground very quickly (though there are circumstances in which it could, like if it started raining), and so by the time the radioactive byproducts come back down, they have had some time for the shortest half-lives to burn out, and they are diffused over a larger area (so no single spot on the ground gets too much).