I teach upper primary, and have done for so long, that I’m not really able to comment on how they handle reading down the school, however If I wasn’t moving a child up a level, I’d definitely find them something different to read, rather than give the same book over and over.
I have met quite a number of children at my stage of primary who can read every word fluently, but cannot clearly communicate that they have understood what they have read. It is quite common, for instance, for children with ASD to be very fluent readers from an early age, but to really struggle with understanding of a text, particularly when it comes to skills such as inference.
I teach two separate reading lessons, reading for enjoyment and reading comprehension. A child in my class can read whatever they choose from my huge choice of books when reading for enjoyment; novels, comics, puzzle books, non-fiction, picture books, etc.
When decoding texts for deeper understanding, a very able reader might struggle more than a reader who has to sound out and slowly decode each word. These texts are deliberately structured to teach different comprehension skills. A fluent reader might need a more straightforward text than a reader who has to sound out each word.
I currently teach a child, who was reading fluently before nursery and can read anything, who chooses to read books at a much younger level (Horrid Henry) because the child identifies with, understands and enjoys the characters and story at that level. They cannot follow more complicated plots, nor understand the relationships between characters. I have another child who is dyslexic and finds decoding a real struggle, but chooses very challenging novels and painstakingly trudges through, because they love the story and are able to tell me very articulately about what they have read.