It is hard to estimate whether there were enough bombs to kill everyone at any moment. On-ground detonation of entire arsenal of all nuclear powers could cause quite a lot of fallout. It is another question that it would not happen even in a nucleart war, because detonating the nuclear bomb above a military base or a factoy would instantly burn a large area while causing less fallout. So it was considered more effective and more predictable.
It is hard to estimate whether there were enough bombs to kill everyone at any moment. On-ground detonation of entire arsenal of all nuclear powers could cause quite a lot of fallout. It is another question that it would not happen even in a nucleart war, because detonating the nuclear bomb above a military base or a factoy would instantly burn a large area while causing less fallout. So it was considered more effective and more predictable.