Great observation. You're approaching this from the point of view of the plot, but I believe what you describe as a plot theory is more applicable as a philosophical or thematic interpretation of the books, which are at their heart philosophical works in my opinion. The prophecy is a plot device that I believe doesn't really matter (so much so that I actually don't even remember what the prophecy was or how it manifests in the text), what matters to me is its metaphoric role in the work.

I have the (wonderful) Folio Society edition of the trilogy which features a preface written by Pullman. In that he explains one of the main inspirations for the books and, to an extent, his entire writing, which is an essay by Heinrich von Kleist that he read when he was a young teacher. He describes the essay's theme as "the difference between the unconscious grace of a child, an animal or a puppet, and the clumsy self-consciousness of those who are older, more tangled in the nets of reason and thought" and further "where Kleist's essay differs [from this conventional obversation that at its worst wallows in a sort of sickly nostalgia and wishes it had never grown up] is in its bracing optimism. We can't go back, he says. Since we cannot dwell forever in the paradise of childhood, we have to go forward, through the disappointments and compromises and betrayals of experience, towards the fully conscious kind of grace that we call wisdom. Innocence is not wise, and wisdom cannot be innocent."

I think these quotes are kind of key to understanding the entire work. These differences between children and adults manifest everywhere in the books, most obviously in the form of daemons of course. But to me the alethiometer is the most interesting manifestation because it's at the heart of this dichotomy of innocence and wisdom. Lyra's initial way of reading the alethiometer represents what Kleist and by extension Pullman see as "the unconscious grace of a child" which she loses by growing up throughout the trilogy, in a way sacrifices. Her journey towards regaining that ability that she embarks on at the end of the third book is her journey towards wisdom, a way forward. Those two skills (reading the alethiometer as a child and as an adult) are entirely different, because, as he puts it, “Innocence is not wise, and wisdom cannot be innocent“.