Is it correct to say "I write children books" (not possessive case)?

Although Children's books is what everybody says, I would like to understand why the genitive case is applied in such case.

If I write books for children, children is an adjective here; not the owners of my book! The word "children" just defines or characterizes the type of books I write. Therefore, it's an adjective.

So, I understand that genitive/possessive case ("I write children's book") is incorrect grammar.

My question is: is the genitive case here really accepted as right? If I use "I write children books" (following the grammar principle) as as I say "I write pets books" (books about pets, and not possessions of pets) - would I be incorrect? Why?