I have no idea what these algorithms might be are and neither do you. Accordingly I don't see any basis for speculating what will they allow.

Well, let's think about whether we have a proof of concept. What's an example of a generalization about high-complexity algorithms that might show most of them to be easily usefully compressed, for an observer living inside one? At this point it's OK if we don't know that the generalization holds; I just want to know what it could even look like to discover that a universe that looks like ours (as opposed to, say, one that looks like a patchwork or a Boltzmann Braintopia) is the norm for high-complexity sapience-permitting worlds.

ETA: Since most conceivable universes are very very complicated, I'd agree that we probably live in a very very complicated universe, if it could be shown that our empirical data doesn't strongly support nomic simplicity.

The default rule is that "man is the measure of all things" so presumably you are using these words in the context of what is short and simple for the human brain.

No, I'm saying it's short and simple relative to the number of ways a universe could be, and short and simple relative to the number of ways a life-bearing universe could be. There's no upper bound on how complicated a universe could in principle be, but there is a lower bound, and our physics is, even in human terms, not far off from that lower bound.