That simple infinities in time or space* trivially produce Boltzmann brains identical to my own and thus I cannot tell if I am the me in the now or one of the copies that mistakes themselves for me, and that Boltzmann brains are necessarily more chaotic than anything else in their ongoing experiences (to the extent they get to have any at all), producing every possible variation on not just good futures but also bad ones, and there are more possible bad futures.
On the plus side, the whole thing with Boltzmann brains also says that if they exist you can't trust the logic that makes you think they exist, so the universe is probably not only not infinite but also small enough that Boltzmann brains can't form. No Poincare recurrence in time, and no Tegmarkian replica of our Hubble volume 10^10^115 meters away let alone Tegmark's higher levels of multiverse.
* and also quantum mechanical multiple universes, but they're more esoteric
