Nice try
... but headline misses the mark.
Nuclear war won't solve the pension crisis, because the hit to GDP would be greater than the hit to population. Given the distribution of wealth, it may well be that the older population survive in disproportionate numbers.
Even assuming some means can be contrived to keep paying pensions, and even if there isn't a complete breakdown of money and banking, they'd still be worthless because nobody would be making Tetley's and carpet slippers and the Daily Telegraph any more.