I don't think the Doomsday Argument is that interesting. It may be trivially true, but it doesn't tell us anything interesting or predictive.
If it is true, it can let us put probabilistic upper bounds on the future of the human race. For instance with 99.99999% likelihood I can tell you that the human race will fail to succeed in expanding colonization of other stars. As much as we may dream of the stars, we will never reach them.
Similarly the odds of our maintaining our current population levels for the next thousand years is something like 40%. That is both interesting and predictive. Its meaning, however, is highly debatable.
If someone gave you a trick coin, and you didn't know which side was favored, you'd have to assume 50/50, even knowing that you were certainly wrong. Knowing that one side is weighted doesn't give you any interesting information for one toss.
If you follow the arguments for and against the DA, it's clear this isn't about a well-defined statistical argument, but immediately devolves into qualitative arguments about our survivability. The optimists say, well, based on the average extinction rate it's extremely unlikely we'll die in <100 million years. The pessimists counter that we're creating technologies with extinction level capacities very rapidly. Either way, we don't have a way of gauging the predictive power of these claims. We can't run a controlled study of 100 human species spans.
And that's fine, because we need to argue about and introspect on the longevity of species, but brainteasers like the DA don't further it in any meaningful way.