I’m not professional, but I have been playing for awhile and can sight-read fairly easily. What you said here is 100% true, and I liken it to learning to read a language. Watch how kids learn to read, they have to look at each syllable and letter and sound out each word. Eventually, after enough practice, you don’t read individual letters, you read words. Then, you begin to observe the nuance of the grammatical structure.
I feel like reading music notation has followed a similar trend for myself. I no longer read individual notes, I see chords and progressions. Just like stories tend to follow a plot line, and you can predict how the story may end, music follows a plot line, and you can predict the movement. This is also why certain styles of music is so interesting! We expect the plot to move in a direction and then are surprised by the twist. This video by 8 bit music theory gives a good overview of how that can be done[0].
I especially love when I’m playing through a new piece and every part of the song just makes sense. Yiruma’s music in particular feels very natural for me, and it’s an absolute joy to play through the song and have it all flow together so well.
Anyways, I think a lot of people just don’t give it enough time and give up a bit too early. It’s magical when you pass that point of reading individual notes and enter into the territory of really reading pieces. I still have so far to go, but music will always be a relaxing and fulfilling hobby.