The Doomsday Argument is premised on the idea that one should reason as if they are randomly selected from the set of all actually existent observers (past, present and future) in their reference class. If we consider ourselves as randomly placed in the birth rank, then we should expect a doomsday event soon.
However, it seems that we should include the idea that one can reason about anthropics and maybe that one actually does reason about anthropics. Also, we could consider observer moments (OM) reasoning about anthropics. If we do this, then perhaps it is not AI that will kill us but enlighten us about our future or some central question about humanity. OM reasoning about anthropics could fall simply because nobody feels it necessary with superintelligence because all these sorts of questions are better answered through AI.
I think aturchin had a similar idea where people simply lose interest in the DA.