Computational complexity would seem to provide a limitation deeper than mere physics. The sentence "John did a huge amount of computation" doesn't perform any computation. It doesn't do any work of any kind, except as interpreted by some reader via their own computations.

if the basis of this whole line of reasoning is anthropics on steroids, then the fact that our universe is limited by computational complexity does imply that other places in the multiverse will, too. In fact, if computational-complexity limits on computation weren't universal, than the vast majority of measure would be in worlds without such limits, since those universes could host arbitrarily more stuff. And yet we find ourselves in this world.