Hi Primulas, what age/year is your DS?
At our school there is a 'read every book in every level' policy too, and they have LOTS of books, which means that by now, lots of children are on book bands well below what they can read (and do read, outside of school). Think children happily devouring Harry Potter books but stuck on gold level school books.
Parents were (collectively) told off by the headteacher, two years ago, for asking the teacher to assess their child's reading level, so very few do, now. But I have noticed that very occasionally, a child gets moved up levels despite not having 'finished' that level, and suspect that it is because that child's parents 'dared' to ask anyway. And the teachers, in general, are very reasonable and do not mind doing it.
So you could definitely put in a gentle word with the teacher, saying you've noticed your child has become very confident with reading recently, and is reading x and y at home, and would they possibly mind checking if they are on the right school book level?
If that isn't successful, your strategy depends a bit on how old your child is.
If your DS is reading turquoise+ and is in reception or Y1, I for one would just keep on with the daily reading of the school books, whilst providing them with more interesting reading material at home.
DS is summer born and was on purple at this stage in Y1. He could have read much harder books but as you move up the levels, the books become 'older' regarding their interest levels as well. So I was fairly happy for him to continue on 'easy' books rather than having to vet each school book as to age appropriateness beforehand. I didn't want him to be reading books aimed at 10-11 year olds at age 7, or so. So we just enjoyed not having to struggle with reading, and being able to use the time thus gained to explore the vast range of brilliant books for young children that is out there. Similarly, he spent ALL of Y2 on Lime books, and read all 150+ that the school own. I never pushed for him to be moved, until he was being given the same ones again.
(Even so, he is now, still 7, reading school books aimed at 10yo+. That's despite me slowing down his school reading progress rather than pushing to speed it up.)
At home, in contrast, he has been developing marvelously as a reader. The school books have not done him any harm, either; they are short, quick reads that nevertheless give him some breadth and awareness of many types of stories and lots of non-fiction topics, and keep him reading when he is in a rut between books he loves. Without ever becoming taxing and eating into his time too much.
In contrast, if your child is in Y3+ and on turquoise school books, but reading chapter books at home, I would push harder with school. And if they refuse to give him reading books that match his abilities, due to some silly 'policy', then I'd consider not making him read those books at all and providing him with appropriate reading material at home instead. Whilst explaining to school that this is what you are doing, so as that he won't get in trouble for it.