I’m always skeptical of hypotheses that use infinities like Many Worlds Interpretation and an infinitely big universe, in part for this reason.
I wonder if the ideas about the universe being infinitely big are a holdover from the days before the Big Bang was universally accepted. For whatever reason, people couldn’t let go of the idea of an infinitely big universe even as the Big Bang became the consensus, so they came up with the idea that the universe is infinitely big but still expanding. (Which honestly seems like a contradiction in terms to me.)