Most of the arguments in favor of the Boltzmann Brain are written before the discovery of the Hubble's law (1929) when most people thought that the universe was essentially eternal and static. Even Einstein was trying to use the cosmological constant to save the model of a eternal static universe.
After the discovery of the Hubble constant, the Big Bang and Inflation, it's more razonable a low entropy starting point.
> arguments in favor of the Boltzmann Brain are written before the discovery of the Hubble's law (1929)
I'm pretty sure the Boltzmann brain paradox is 20th century, likely originating with John D. Barrow and Frank Tipler -- they discuss it in e.g. chapters 6 and 10 of their 1986 book on the anthropic cosmological principle, although afaict the actual words "Boltzmann['s] brain[s]" first popped up in the early 2000s.
Dyson, Kleban and Susskind (DKS 2002, https://arxiv.org/abs/hep-th/0208013) is firmly after the widespread acceptance of the lines of evidence pretty much compelling an accelerated expansion of the universe, for example. Albrecht & Sorbo actually talk about brains and bodies and so forth in 2004 https://arxiv.org/abs/hep-th/0405270v2 : in section "C." they discuss some of the history of the paradox, briefly.
Without a finite age to the universe -- this comes from Lemaître in 1927, rather than Hubble in 1929 -- there is no particular reason to assume that there is a low entropy state in the past. A positive cosmological constant creates more empty space (all of which is very high entropy, because of the indistinguishability of subregions of any region of truly empty space) and thus demands a much lower entropy before the dark energy dominated era. It's the low entropy of the past that's the source of concerns about Boltzmann brains. And a hot big bang is even worse. How did the universe end up in such relatively low entropy? And it must be low entropy rather than a hot dense system in equilibrium, because otherwise one runs into the problem of suppressing Boltzmann brains.
He didn't know the Raychaudhuri equations (1955, shortly after his death) or the focusing theorems they support, only the Jeans equations (1902), and was trying to suppress a collapse via Jeans mechanisms. Had he known about Raychaudhuri's expansion scalar, who knows where he would have went -- perhaps he might not have discarded his small negative cosmological constant in the aftermath of evidence for the expanding universe, but rather might simply have accepted a small positive value as consistent with the evidence and theory, and we wouldn't have had to wait half a century to get it back in the minds of cosmologists. On the other hand, perhaps we would still have had to wait for the discovery of the accelerated expansion to get to a small positive cosmological constant as a parsimonious explanation.
After the discovery of the Hubble constant, the Big Bang and Inflation, it's more razonable a low entropy starting point.