> you could compress text to an equally random sequence

More or less correct. The key difference is that you could not compress a random coin flip sequence (and that a compressed text is meaningless until decompressed to original).

> all minimal programs are by definition Kolmogorov random

Compression provides an upper bound to K. Kolmogorov Randomness itself is not computable. AKA: You can't ever know if you have a minimal program.

> Crystalline forms

It is possible to both have low significance and low information content. Crystalline forms were very significant to Turing though: https://en.wikipedia.org/wiki/The_Chemical_Basis_of_Morphoge...