I think it's a bizarre thing to do as school policy. One of my last things every school year is 'here's your most recent book - if you want to keep it, help yourself. If not, please rip out the used pages & dump them in this box for recycling, & the rest of the book in this box for scrap paper.'
I keep a drawer full of 'scrap' exercise books & all my classes know that if you forget your book, just grab one out of the scrap drawer, then make sure you glue the work in your own book at the first opportunity.
I teach secondary, & we have a half-termly 'book check' by HOD to ensure we're doing a good job in terms of marking & feedback - one year group each half term.
In practice, each member of the Dept. takes it in turns to do the book check alongside HOD, so we're all involved.
This is just the routine exercise book marking - moderation of GCSE controlled assessments etc is quite a bit more involved!
Then there's an SLG book check each half term too, which consists of checking every member of the teaching staff - you get an email the night before to let you know that you need to send a particular set of books in following the lesson.
Should you be behind with marking for this group, & the kids have the books for homework so you can't do a quick mark prior to lesson, you are at this point destined to receive a Pained Email, & it's a black mark on your Performance Management.
My books are always sufficiently up to date to pass muster, which means sometimes I have to rush through them. I can mark a set of 30 books to 'book check' standards in an hour, whereas marking them 'properly' & in a manner genuinely helpful to the student takes at least twice as long.
So I have no fears of parents seeing my books because they don't 'look marked' & I don't imagine any of my colleagues would either.
Very odd! My dc's primary school sends them all home. I give each dc my phone & invite them to snap as much of their work as they want to preserve - as a folder on my PC - before the books go in the recycling.