[jerf]

"Does it tell us anything about the universality of computation as a property of the universe?"

It tells us that computation is counter-intuitively easy to access. Our intuition says that computers are hard; look how hard they are for us to build, after all! But instead the reality is that if you try to exclude computation from a non-trivial system, it's actually fairly hard.

(I think part of this intuition may also be based on our intuitive experience mostly being with von Neumann machines. Contra some other contrarians, I think we work with them for a good reason; as wild as they can be, they are much tamer than many other systems capable of universal computation. Compare with trying to work in Rule 110 directly as our primary computation method, or cellular automata in general. Many of these accidental TC systems are very strange and would be hard to work with. Getting a universal computation system nice and friendly to humans accidentally is pretty hard. Getting a universal computation system without that qualification is like falling off a bike.)

https://www.gwern.net/Turing-complete is a good overview both of this concept, and includes many interesting consequences. I also particularly recommend the section title "Security Implications".