It sounds really interesting - however, I can't help but wonder that this doesn't necessarily come to anything deeper, that this kind of theory where any of these rules can be arbitrarily chosen and ultimately comes down to some kind of Turing-complete automata just uses the "computational possibilities" of this theory to arbitrarily arrive at the physics we know.
Maybe that wasn't super coherent, let me explain. Like this theory basically posits the universe as a kind of machine that is just executing these rules over and over. But we don't know what those rules are. But I feel like the inherent "computational power" of these theories just let them come up with the laws of physics through sheer brute force.
I mean, if there's essentially an infinite amount of possible rules, then of course some rules exist that would fully explain our known physics. That doesn't mean that those are the rules by which the universe works, it just means that you have found some kind of "compressed" version of physics in a ruleset. I'm not sure this is really any deeper insight.
Also, isn't there a problem in that this theory doesn't seem to be able to be used for predictions? From what I understand, it seems that there is essentially no way to "simulate" the propagation of the rules without actually executing the rules, essentially. Like you can't just simulate a ball falling, you need to actually have a ball and let it fall in order to see what happens. But maybe I'm not understanding it correctly.