I like introducing the uncertainty of what is or is not real (like Inception). That could turn it into a paranoid thriller like some Philip K. Dick stories.
(Psychics in sci-fi: Foundation, Ringworld, Akira and about a million other animes, The Demolished Man, The Stars My Destination, Dune, loads of Phillip K Dick, Starship Troopers,... If you read a lot of 20th century sci-fi it comes up A LOT.)
The Oracle had realized years before that this could be used to relay shutdown commands to nearby machines because relatively lax security on this port and had built in the capability into "the one" as a failsafe.
In fairness to the Wachowskis, they do literally explain this in the movie, in literal dialog, in the third Matrix film.
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Neo: "Tell me how I stopped four Sentinels by thinking it"
Oracle: "The power of the One extends beyond this world. It reaches from here (i.e., the digital matrix) all the way back to where it came from (i.e., in the real world).
Neo: "Where?"
Oracle: "The Source. That's what you felt when you touched those Sentinels"
The sentinels are networked (in the real world) and Neo has god-like access (superuser). Superuser works inside the matrix, but it also works on anything connected to the Matrix or networked to the matrix (like the Sentinels are, like most of the machines are).
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Most people just tune out the dialogue about philosophy in these films, and then complain that nothing was explained. (when like, most of it was explained, folks just got bored and stopped listening)
That's fine in Matrix 1, because Matrix 1 works as a film even if you ignore the philosophy dialogue. Matrix 2, 3, and 4 are pretty good too, but they only work if you are also paying attention to all the philosophy dialog.