You present a bare assertion as a premise of your analysis.
Why should we agree with this? It seems obviously false. What evidence do can you present to support this assumption?
There are examples of non-designed processes processes we can directly observe producing FI. We can observe high amounts of FI in cancer evolution too, which you agree is not designed. We also see high amounts of FI in viruses, which you also agree are not designed. All these, and more, are all counter examples to your assumption.
As a technical point, without clarifying precisely how FI is defined, this is not at all clearly the case.