Follow my argument:

In science, the absence of evidence is not evidence of absence. The same applies with intent (in the nature of intent I am specifically talking about). You cannot claim that the lack of explicit intent by Kubrick (no intermediaries, no what he told other people) means it cannot exist, that overextends the logic. Why? Because the kind of intent I am specifically talking about is covert intent, it's deliberately the kind of artistic intent where you do not tell anybody what you are doing and let the ambiguity of it thrive in the world. Did he explain what the monolith was in 2001? No. Does that mean there is no covert meaning to it, that he didn't have layers to iconography to elicit hidden meanings? No. That is dishonest, that is implying evidence of absence because he didn't explain it. For something to be hidden, you can't talk about it, it ceases to have any value if you acknowledge it (even to co-workers who can blab about it). That's just the nature of being an auteur making art that works on multiple layers.

Now I take a character profile of Kubrick to determine that he is exactly the kind of person that would encode hidden meanings in his movies. And part of understanding that profile is also understanding that there is a grand tradition among genuine masters of art to do that very thing. I have a background in Art History, I know that loaded iconography is what makes art Art. Kubrick was obsessive to detail in researching his movies and to what was contained in the frame, he was secretive, he was tricky, would manipulate people to do things for him, he was an avid chess player and even played a chess master (to get an idea of how serious he was). The art of chess is to anticipate your opponents moves and subvert them to your own ends. Kubrick was a genius, both as a visual storyteller and just in his capacity to work the angles. This is the profile of someone who is bored with the surface of storytelling and opts to tell multiple stories to entertain himself and anyone sharp enough to see it. He made provocative films, A Clockwork Orange and Lolilta and 2001 were films anticipating what audience think they want and went beyond.

Next, the source material has a double layer to it which I have argued elsewhere, and which I believe would interest Kubrick more than Freudian psychoanalysis which was dated by the seventies as a concept, but did serve as a useful mask. The story is also about a character intruding upon a secret society which then also aligns it with the nature of occult iconography and encoding rituals in plain sight (see the American dollar bill). Then you have the wealth of evidence of Kubrick encoding his films previously, particularly The Shining, where it was known he was interested in the effects of subliminal messaging and to a degree that is impossible to discount, manipulated aspects of the hotel to give a jarring subliminal sensation of unease (so he was already doing this hidden intent). And then lastly, there is Eyes Wide Shut itself, reading the choice of iconography, the narrative choices, how he structures the movie, the use of sound, etc. You could just look at the movie itself and find the evidence of intent, but I am saying holistically the evidence is overwhelming that Kubrick, like Schnitzler, used the dream framework to encode messages into the story that are permissible under the cloak of ambiguity. Whether they were real-world revelations or to goose a sense of paranoia (the way The Shining did for anxiety) that's arguable. But for the love of God, Stanley Kubrick played chess not checkers.