It's sounding like a Boltzmann brain... the observer who happens to have memories of Born-friendly statistics should still be blasted into random pieces in the next moment.
I haven't pinned down the logic of it yet, but I do believe this issue - that the validity of quantum statistics is required for anything about observed reality to have any stability - seriously, even fatally, undermines Wallace's argument. Consider your assumption 2, "Arbitrary quantum superpositions can be prepared". This is the analogue, in the decision-theoretic argument, of Bohr's original assumption that there is a classical world which provides the context of quantum measurements. That assumption is unsatisfactory if we are trying to explain, solely in terms of quantum mechanics, how a "classical world" manages to exist. It looks the same for Wallace: he is presupposing the existence of a world stable enough that an agent can exist in it, interact with it, and perform actions with known outcomes. We are told that we can get this from Schrodinger dynamics alone, but Schrodinger dynamics will also produce nonzero amplitudes for all the configurations where the world has dissolved into plasma. Since we are trying to justify the Born rule interpretation of those amplitudes, we can't neglect consideration of these disintegrating-world branches just because the amplitude is small; that would be presupposing the conclusion. Also, observer selection won't help, because there will be branches where the observer survives but the apparatus disintegrates.
It all sounds absurd, but this results directly from trying to talk about physical processes, without using the part of QM that gives us the probabilities. When we do use that part, we can safely say that the spontaneous disintegration of everyday objects is, not impossible, but so utterly unlikely that it is of no practical interest. When we try to describe reality without it, then all possible futures start on an equal footing, and most of them end in plasma. I just do not see how the argument can even get started.
The decision-theoretic argument is not supposed to prove everything. It's supposed to explain why agents living in environments that have so far been stable should set their credences according to the Born probabilities. So, yes, there are presuppositions involved. But I don't see how this is a devastating problem for Everettianism.
You brought up Boltzmann brains. It turns out that our best cosmological models predict that most observers in the universe will be Boltzmann brains. The universe will gradually approach an eternally expanding cold de Sitter pha...
The subject has already been raised in this thread, but in a clumsy fashion. So here is a fresh new thread, where we can discuss, calmly and objectively, the pros and cons of the "Oxford" version of the Many Worlds interpretation of quantum mechanics.
This version of MWI is distinguished by two propositions. First, there is no definite number of "worlds" or "branches". They have a fuzzy, vague, approximate, definition-dependent existence. Second, the probability law of quantum mechanics (the Born rule) is to be obtained, not by counting the frequencies of events in the multiverse, but by an analysis of rational behavior in the multiverse. Normally, a prescription for rational behavior is obtained by maximizing expected utility, a quantity which is calculated by averaging "probability x utility" for each possible outcome of an action. In the Oxford school's "decision-theoretic" derivation of the Born rule, we somehow start with a ranking of actions that is deemed rational, then we "divide out" by the utilities, and obtain probabilities that were implicit in the original ranking.
I reject the two propositions. "Worlds" or "branches" can't be vague if they are to correspond to observed reality, because vagueness results from an object being dependent on observer definition, and the local portion of reality does not owe its existence to how we define anything; and the upside-down decision-theoretic derivation, if it ever works, must implicitly smuggle in the premises of probability theory in order to obtain its original rationality ranking.
Some references:
"Decoherence and Ontology: or, How I Learned to Stop Worrying and Love FAPP" by David Wallace. In this paper, Wallace says, for example, that the question "how many branches are there?" "does not... make sense", that the question "how many branches are there in which it is sunny?" is "a question which has no answer", "it is a non-question to ask how many [worlds]", etc.
"Quantum Probability from Decision Theory?" by Barnum et al. This is a rebuttal of the original argument (due to David Deutsch) that the Born rule can be justified by an analysis of multiverse rationality.