If nuclear weapons followed the same path as the ones in real life, then yu wouldnt need to cover every square mile. There was a survey or something (or some quote) that stated that the Russians (real life, this has relevance) had enough nuclear weapons to kill every living thing on this planet, so why not the US or China in the Fallout Universe?
Actually if a nuclear war broke off in the beginning of the 80s, when the stockpile was at it's highest, and every nuke reached it's target, it would barely kill everyone in the major centers, let alone everything live in the planet. MAD was actually just intended to make the sure losses unacceptable, it didn't really assumed it was possible to completely destroy the world, or even the US/USSR. The nuclear holocaust was really just a myth, a pacifist FUD to prevent a nuclear war (which would me nonetheless disastrous). In reality nuclear weapons are much less powerful than people imagine, and about 80-90% of the expected casualties in a nuclear war would be caused by the famines, diseases, lack of medical services, riots, and etc which would follow the mass panic and governmental disruption, and not by it's direct effects. So no, humans couldn't cause a mass extinction in the planet even if they deliberately tried to.
The radiation from the Nuetron bombs is too intense for it too just "disappear" after a while. In areas where the bombs actually exploded, the radiation would still be intense and lingering.
It's exactly because it's so intense that it's short lived, plus N-bombs produce very little fallout. In neutron bombs there's a short burst of intense ionizing radiation (1 day - 1 week at most), and then residual radiation would fall beneath 10%. After 3 weeks you could spend up to 4 hours unprotected on the ground zero before it becomes dangerous, and 4 more months the area would be fully habitable again.