Given that we agree not to use an assumption of 'typicality', is there any reason to discard a cosmology where the overwhelming majority of brains are Boltzmann brains? (And the majority of stars, planets, galaxies etc. are also Boltzmann-stars, planets, galaxies...)The short answer is No. Here is my longer answer.
Dear Thomas, I don't understand what one can possibly mean by an "overwhelming majority of something in a cosmology". I only know how to measure majorities of people or brains or other objects or creatures who live or exist at the same moment (a thickened slice of spacetime), who interact with each other, and who have some enforced equality or a similar mechanism that makes counting of majorities relevant.
If you want to compute majorities in spacetime as opposed to space, what is it supposed to mean? You face exactly the same problems as with the problematic notion of "typicality" in spacetime because typicality and a membership in a majority is really the same thing.
These majorities are ill-defined
Do longer lives matter more than shorter lives? Do you double-count brains that have been transplated into a different body (if the readers kindly allow me to avoid reincarnation)? Do you discount future votes by a discount rate or, on the contrary, increase their impact because they will be smarter, more sensitive, and more important than the contemporary brains? How do you count majorities if the number of brains is infinite - which is clearly a possibility in a temporally infinite universe?
Do you grant full human rights, including the rights to vote, for the Boltzmann brains even though the circumstances of their birth are much more morally problematic than those of generic bastards and their DNA probably deviates substantially from anyone whom we have ever called a brother or a sister, for that matter? How will the future Boltzmann brains defend themselves against the Boltzmann racists such as your humble correspondent who consider them to be a worthless piece of biological junk rather than subjects that determine majorities? Are you ready to impose and advocate intertemporal Boltzmann political correctness? ;-)
Whatever your answers are, how do you determine that they're the right answers while other answers are wrong? What is the physical meaning of such bizarre rules and calculations of majorities in spacetime? Why should physics care about such rules? How can the rules of mechanics and field theory co-exist with metaphysical laws that are built upon "majority" labels? What is the (acausal) mechanism that allows majorities in the future to beat or overshadow minorities in the past and decide about their fate or the fate of their Universe? Isn't it really obvious that such an action can't exist because of the basic principles of causality?
I think that any statement involving majorities of anything in spacetime has exactly zero physical meaning, so the answer to the question above is that if something holds or doesn't hold for such a bizarre "majority", it means nothing whatsoever for physics. There is absolutely nothing wrong with a theory or a cosmology only because it leads to some bizarre (or socially undesirable) "majorities" in spacetime, probably dominated by some future configurations of matter, and there exists no rational reason why "we should be them".
Many two-headed gay canibals
To see how the "majority" reasoning is absurd, let me ask you about the following gedanken experiment. Imagine that the mankind survives for millions of years and there will be quadrillions of people living in the Milky Way during those later times, most of which will be two-headed gays and canibals. Does it mean that something is morally wrong with our world or a theory that describes it? How could you blame our civilization, our Universe, or the laws that describe them for something that happens or doesn't happen in the distant future? Or do you think that, assuming their existence, these future two-headed gay canibals could change our current gay marriage or agricultural laws just because there will be so many of them? Or do you think that there exists some a priori metaphysical yet rational method to prove that the sketched future is logically impossible or, on the contrary, logically inevitable? You can't be serious.
Whether quadrillions of canibals or Boltzmann brains evolve in the year 1,000,000 or not has absolutely no implication and cannot have any implication for our behavior today and for our rational decisions about the validity of theories that describe our Universe. Only the presently available observations, possibly encoding past events, can influence our decisions and arguments whether individual theories are valid. These relevant effects are called "evidence" and legitimate "evidence" must be something that already exists today, not something that could hypothetically emerge in the future.
Let us insist on causality...
These things may evolve or not but it is a dynamical question that is only relevant for the future, not for the present or our explanations of the past. Any other answer would be acausal and logically absurd because if one admitted a role of the future events for physics such as cosmological evolution, it would also lead to causal loops, i.e. essentially closed time-like curves. Still, it is exactly one of the kinds of absurd and flawed reasoning that the anthropic people misdo on a daily basis.
Future is only constrained by the present and the laws of physics, not by universal metaphysical bans
The future of our Universe can involve an empty de Sitter space (the most likely choice), the Big Crunch, trillions of cycles of a cyclic Universe, Boltzmann's brains, or anything else that the actual laws of physics will lead to. There can't be any inconsistency about the physical laws (or, on the contrary, a selective advantage of certain universes) just because they lead to one particular kind of future or another. The future is allowed to be whatever it will be according to the laws of Nature.
The free-will theorem makes this conclusion particularly clear because the physical systems in the future "freely decide" what to do and the probabilistic predictions of quantum mechanics are the only constraint they must respect. In particular, the future coincidences cannot determine or influence the "prior" probabilities that were deciding about the evolution of anything in the past.
For example, if the climate alarmists are right, and I have no problems whatsoever to think about such far-fetched gedanken experiments, a foreseeable future of life on Earth involves either a cataclysmic warming or a new, carbon-regulating, global totalitarian system (they prefer the latter choice even if the former one were impossible). Does it mean that such a dark future proves that our Universe is cosmologically inconsistent? Is there something wrong with physical laws just because they predict something in the future that we don't like for existential reasons? Does God decide for abortion once She calculates that the distant future of Her Universe looks bleak?
Or are the mechanisms of supersymmetry breaking leading to a very rich Africa in 2050 (that earns a lot of money from the African gravitinos) more likely to be true than the mediation scenarios that keep Africa poor?
I find it obvious that as long as our reasoning is rational, respects causality, and avoids wishful thinking or an implicit or explicit God who is protecting us not from logical inconsistencies but from bad luck, as measured by human emotions, the obvious answer to all four questions is No. These kinds of future, however unattractive for a human, don't mean and can't mean that a physical model is inconsistent or unlikely. And a rosy future doesn't mean that the corresponding model is preferred.
Because of the very same reasons, one can't "derive" the opposite conclusion, namely that the civilization must end soon and only a few more billion people will be born, otherwise we wouldn't be typical. In reality, whether the mankind is going to kill itself or not will depend on the future decisions of people and on the future external physical circumstances, not on a metaphysical, spacetime-wide counting of typicality.
Please, let's not use the speculations about the distant future to determine what could have happened in the past. The past may influence the future but the opposite type of influence is not possible because the events in the past depend, via the laws of physics, on the data in even more distant past, not on the data from the future. Allowing the influences to propagate in both time directions would immediately imply logical contradictions that are familiar from cheap and not-so-cheap movies about time machines.
And that's the memo.