I think the issue might be in what constitute “natural causes”. Precisely the core of Intelligent Design is that “agency” is a “natural cause” (it is observable and testable in the here and now) but not a mechanistic one. See my article on ID as a theory of causation. It’s not the inclusion of new causes that aren’t readily observed — in fact, we observe intelligent causes throughout life. The difference is that Intelligent Design does not assume that intelligent causes are thoroughly describable by mechanistic causes. Therefore, one aspect (but not the only aspect) of ID is to be able to separate causes or components of causes. Interestingly, one ID scientist is already putting the ID concepts of non-mechanistic causes into scientific use that has nothing whatsoever to do with origins. Because ID is not primarily a theory of origins, but rather causation.

“he starts from the position of irreducible complexity, not from the position of the appearance of design”

I think you are misreading what “irreducible complexity” is to Behe. It is not fundamentallly about evolution, but instead about a designed holism. It is an attempt to define empirically what a holistic system looks like. It may not be the best way to do so, but if you read what he is getting at, he is trying to come up with a scientific definition of holism, which is in fact what designers do when designing. The post I referred to earlier makes this case.

Another interesting argument for holism/IC in biology (in the case it is a specific holism — that of self-referential symbolic codes) is Voie’s argument from Godel incompleteness — that intelligent agency is a necessary factor in creating self-referential symbolic codes, and that Godel’s incompleteness theorem proves that mechanistic causes are incapable of such.

ID

IC doesn’t say “this can’t be produced evolutionarily and therefore it was designed”, but rather “this can’t be produced by Random Mutation and Natural Selection, AND it matches what we know about how designers design, therefore, design is a better explanation than Darwinism”.

Also, just to be clear, Behe is NOT arguing that IC systems don’t evolve. In fact, Behe does in fact believe that they do evolve (in fact, most of the leading lights in the ID movement take Universal Common Ancestry for granted), but rather that they evolve by a telic, rather than a non-telic, mechanism. The pure mechanistic version of this idea (at least after the origin-of-life) is known as front-loaded evolution.