The development of nuclear weapons that could wipe out humanity is, as you say, evidence against quantum immortality.
Given the development of nuclear weapons, narrowly avoided nuclear wars are evidence in favor of quantum immortality.
The balance of all this evidence is not clear to me. It depends on how strong each piece is, on how much branch measure from 1750 has humans developing nuclear weapons, and how much from 1950 has incidents that could spark a nuclear war.
The development of nuclear weapons that could wipe out humanity is, as you say, evidence against quantum immortality.
Given the development of nuclear weapons, narrowly avoided nuclear wars are evidence in favor of quantum immortality.
The balance of all this evidence is not clear to me. It depends on how strong each piece is, on how much branch measure from 1750 has humans developing nuclear weapons, and how much from 1950 has incidents that could spark a nuclear war.