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Not the Doomsday Argument, but self-locating probabilities can certainly be useful in decision making, as Caspar Oesterheld and I argue for example here: http://www.cs.cmu.edu/~conitzer/FOCALAAAI23.pdf and show can be done consistently in various ways here: https://www.andrew.cmu.edu/user/coesterh/DeSeVsExAnte.pdf
Just to make sure I understand your argument, it seems that you (dadadarren) actually disagree with the statement "I couldn't be anyone except me" (as stated e.g. by Eccentricity in these comments), in the sense that you consider "I am dadadarren" a further, subjective fact. Is that right? (For reference / how I interpret the terms, I've written about such questions e.g. here: https://link.springer.com/article/10.1007/s10670-018-9979-6)
But then I don't understand why you think a birth-rank distribution is inconceivable. I agree any such distribution should be treated as suspect, which probably gives you most of what you need for your argument here, in particular that the Doomsday Argument is suspect. But I don't see why there would necessarily be some kind of impenetrable curtain between objective and subjective reasoning; subjective facts are presumably still closely tied to objective facts. And it even seems to make sense to discuss about purely subjective facts between subjects -- e.g., discussions about qualia are presumably meaningful at least to some extent, no?
Nice provocative post :-)
It's good to note that Nash equilibrium is only one game-theoretic solution concept. It's popular in part because under most circumstances at least one is guaranteed to exist, but folk theorems can cause there to be a lot of them. In contexts with lots of Nash equilibria, game theorists like to study refinements of Nash equilibrium, i.e., concepts that rule out some of the Nash equilibria. One relevant refinement for this example is that of strong Nash equilibrium, where no subset of players can beneficially deviate together. Many games don't have any strong Nash equilibrium, but this one does have strong Nash equilibria where everyone plays 30 (but not where everyone plays 99). So if one adopts the stronger concept, the issue goes away.
But is that reasonable reassurance or just wishful thinking (wishful concept selection)? Really answering that requires some theory of equilibrium selection. One could consider learning algorithms, evolutionary dynamics, some amount of equilibrium design / steering, etc., to get insight into what equilibrium will be reached. My own intuition is still to be cautiously optimistic about folk theorems, since I generally think the better equilibria are more likely to be selected (more robust to group deviations, satisfy individual rationality by a larger margin, etc.). But I would also like to have a better theory of this.
Great discussion! Just pointing out two additional relevant references:
Aumann, Hart, Perry. The Absent-Minded Driver. Games and Economic Behavior, 1997.
Korzukhin. A Dutch Book for CDT Thirders. Synthese, 2020.
The first one also discusses how optimal policies are consistent with CDT+SIA. Both give examples of other policies being consistent with CDT+SIA too.