our universe is so suspiciously simple and regular relative to all imaginable universes

(Assuming you mean “all imaginable universes with self-aware observers in them”.)

Not completely sure about that, even Conway's Game of Life is Turing-complete after all. (But then, it only generates self-aware observers under very complicated starting conditions. We should sum the complexity of the rules and the complexity of the starting conditions, and if we trust Penrose and Hawking about this, the starting conditions of this universe were terrifically simple.)