We know entropy != Complexity(1). There's still no satisfactory answer for what complexity is, and the problem is only getting worse I think as more people decide to use the term however they wish. I'm partial to kolmogorov(2).

You're train of thought re. compressibility vs. organization is very in line with kolmogorov's.

1.https://www.taylorfrancis.com/books/mono/10.1201/97804295028... 2.https://en.m.wikipedia.org/wiki/Kolmogorov_complexity