Great post, you're clearly on the right track. I totally agree that there is a major gap in modern theoretical understanding of how and why complex systems emerge. Breakthroughs in understanding the physical/informational processes that underlie complex adaptive systems could be immensely useful.

I'll add a word of caution though. I'm most familiar with systems theory applied to biology. Biology is, in my opinion, the pinnacle of complexity. However, it's less well acknowledged that it's also very, very complicated. This is important because it means that we have very incomplete knowledge of the base components of any biological system. Like we still don't really know the basic biochemical function of most proteins. Hell, we only just got a partial view of what most proteins even look like (in isolation) via AlphaFold. Measuring the number of all of the proteins in a single cell is effectively impossible with current and near future technology. Any feasible solution for this would probably be destructive, meaning that true time-series measurements are also impossible. These details of what we know and what we can (or can't) observe matter quite a lot, not only because they are the sort of raw matter of a systems theory, but also because they are the levers that we have to use to manipulate the system. There are only about 1000 proteins that we know how to reliably bind molecules to. There are (probably, we're not sure) more than 50k different proteins, if we include isoforms. So, all that to say, we have very incomplete knowledge of biology and very incomplete control of cellular behavior.

This isn't meant to discourage you! Instead, I think there's a tremendous opportunity for systems theory to be really useful (especially in biology) if it becomes a practical, routine analysis like statistics. But, for that to happen, we have to keep in mind the limitations and specific details of the system we're dealing with.