You're making the same mistake as the researchers who invented "three cueing". They asked themselves "what do I do when I read?" and tried to reverse-engineer a teaching method. Well, turns out that approach doesn't work very well. Part of this may be that "how you think you read" isn't actually how you read. There's plenty of experimental evidence that adept adult readers do use letters as cues rather than "holistically recognizing the word". You could be an outlier but I doubt it.
Anyway, empirically, it's quite clear that phonics works and the "whole language" approach (which "three cueing" is an example of) doesn't. One of the main reasons teachers in the US continue to avoid phonics is that they don't like teaching it.
I absolutely suspect that most adult readers myself included use letters as clues for recognizing the shape of the word. What I dispute is that reading necessarily goes letters->sound recognition->meaning / understanding.
I suspect for myself and many others it goes letters->word shape recognition->understanding ->then last part is sound in my mind's ear.
Infact when I am writing and reading I find myself thinking about the shapes of printed words. I don't even consider what they sound like except maybe in retrospect.
Maybe I am an outlier.
To me it makes logical sense. When I read a word I see the word in my mind's eye (eg m i n d) and hear the word after an after effect.
Printed text is a visual item. Meaning need not have a sound associated with it. It makes sense to go directly from vision to recognition of meaning. I don't need to know what words sound like to understand their meaning. As a kid I took Latin and Ancient greek. Honestly I don't think anyone knows the precise phonetics as they were spoken at the time of these ancient languages and yet that is no impediment to understanding the meaning of word by reading the written word with your eyes. There is no need for phonics in reading. It's based on the misunderstanding that the sound is the unique vehicle of meaning when it need not be.