OP, DS was anxious in Y1, and we were told almost the exact same thing ('keep him on this book level as otherwise we won't have anything for him to move on to next year'). Also suddenly a new rule that all children must read every book in every level, so unless he did actually read those books (it was purple level this time of Y1 for us) he would never move up the levels. So I can relate.
You don't say much about his ability in other areas so I will respond to the reading only. What I would say is that you need to be careful to distinguish between 'progressing in the book levels' and 'progressing with reading'. Holding a child back in the book levels is not equivalent with holding their reading back.
Conversely, putting a child on a higher level is not the same as stretching/challenging them!
Chances are that they are challenging/stretching his reading ability at school, they want him to make progress. It's just that you don't see it and it's not easily measurable / comparable like the book bands.
Also, there comes the point where your child 'can read'. What further stretching/challenging should there be then? In my opinion the main aim then is to develop the child's breadth of reading material and give him/her insights into different genres and the kind of storylines and formats that are familiar and common, without moving on to 'literary analysis/criticism' or some such. So it is no longer about 'stretching' or 'challenging', but about reading for pleasure and discovery.
With a competitive child, I think it is important to make the distinction between 'reading ability' and 'book level' clear to them too. And to stress that neither is a race, and that the aim of increasing your 'reading ability' is not to get good grades and praise, but to be able to access fun and interesting books.
Unfortunately at our school the children were making a lot of competitive comparisons regarding their book levels amongst themselves. Possibly this is happening at your school too. In which case I can understand that a child who is moved back levels would feel upset!
So I would mention to the teacher that perhaps a talk is needed for her to remind the children (not just yours!) that neither going up the levels, nor learning to read, are competitions.
Perhaps a way to bring across that the book levels are not a competition is to ask your child: So what is the reward for moving up a level/moving to 'free reader'? You get to choose your own books. Well, you get to choose your own books already. The level of your school reading books does not stop you from choosing to read whatever you like!
Fortunately, reading is one of the easiest areas for you to fill the gaps when the school doesn't. As people say, just use the library ;) However I want to say, I do get your point about the school books then becoming a distraction and nuisance. There is a certain point where the school books have a length that means you can't just whizz through in 3 minutes, but are still rather simple and boring/off-putting. They feel very much like a waste of time, time that could be spent reading more interesting/fun things. And it makes reading feel like a chore, rather than a pleasure.
Firstly, I would like to reassure you that this phase passes. Your child will learn to recognise a simple text and read it very fast. (You are lucky in a sense to have only 2 school books, we had 5 a week, it was a drag!) Or you ask school specifically how much time they expect your child to be reading school books per day (there may be a homework policy on this point too), and then do exactly that. If it is 10 minutes a day, but the books require 30 minutes to finish, just don't finish them - use your time for other, own books.
The point of the reading scheme books for your child then becomes the lesson that school requires you to jump through certain hoops, which you do (in most cases) - building up some 'homework discipline'. After doing the required, you do what you enjoy!
We are now 3 years down the line. In Y3, they finally let DS move onto 'KS2 books' and in fact straight onto the highest level of these, so books aimed at Y6. Some of these are great, they are books just like any other he would read for pleasure/out of interest. Some are highly inappropriate. In some ways I wish they were still 'holding him back'! But at this stage school is more relaxed about the school reading books. I only actually ask DS to read his school book when he happens to be in a reading slump between books/series that he chose for himself.