Wild speculation: Perhaps one could also attempt to explain the effectiveness of mathematics the other way around: Why are the rules of physics simple enough so that we can describe them fairly accurately? I think this stems from the fact that complex systems are often the substrate for simpler systems. There are plenty of examples for this: Simple lifeforms emerge from biochemistry, planets are on elliptical orbits around stars as the result of countless particle interactions and so on. Perhaps this can be explained by the minimum total potential energy principle, that simple rules happen to be the ones which are stable or at least metastable and more complex systems would need more energy to maintain the relationships between its constituent elements. Simple systems can be abstracted from the substrate to the degree they are a reliable phenomenon. The human brain is a rather reliable information processing system, but it's also rather limited in capacity (it certainly has many times less capacity compared to the systems we are able to reason about). However, since the rules of most physical systems happen to be rather simple and since the language of mathematics allows us to compress rules into efficient chunks which fit into the working memories of the brightest humans, we are able to describe physical systems with counter-intuitive effectiveness.
Simple doesn't necessarily mean easy to understand, particularly when the thing doing the understanding is part of (and constrained by the rules of) the system being analysed. It is conceivable that there are simple aspects about our universe we will never understand because they are hidden behind some threshold of observation.
Exactly. I was trying to say that equivalently to "the unreasonable effectiveness of mathematics", we could also wonder at "the unreasonable simplicity of physical laws" (simple in the sense that we are able to understand the properties of it—at least superficially, but often also deeply). There is perhaps also an anthropic principle here: If the systems we find ourselves in would be much more complex, life would have likely been unable to form as prediction and organization would have been too difficult.
It's actually hard to quantify simple systems so perhaps I should have replaced the word "most" with "many" in my comment above. There are also typos e.g. s/its/their/, sorry for that.
