That's just a special case of a general feature of probabilistic arguments: a small but positive fraction of the times they are used, they will give wildly misl

That's just a special case of a general feature of probabilistic arguments: a small but positive fraction of the times they are used, they will give wildly misleading predictions. If we assume that everyone uses the doomsday argument with a uniform improper prior on the total number of people who will ever live, then all of them will conclude with 95% probability that they are not one of the first 5% of people to ever live (that is, that no more than 20 times the past population will be created in the future), and 5% of them will be wrong, which is exactly how probabilities are supposed to work.