Couldn‘t there be something between chaotic and completely random, let’s call it correlated, where e.g. (conditional) independence structures are similar in real-world problems?
You mean something that is well behaved in practical situations but intractable in general?
There is plenty of stuff like that, things don't even need to be chaotic for that. Anyway, chaotic and random are just two specific categories. There are many different ones. Nature happens to like those two (or rather, not random exactly, but it does surely likes things that look like it), that's why I pointed them.
