We have these in Germany.
What usually happens is that a small group of people assume responsibility for the box, so that it's not all on one person.
The people responsible visit the box every few days and tidy it up, remove anything unsuitable (damaged books, rubbish, ripped comics etc) arrange books into genres, and remove anything that's been sat there for months and ignored (I'm not sure how they do this exactly, maybe just by gut feeling) - that means people are actually likely to look through and take things, because it's not impossible to sort through. Children's books are also placed on the bottom shelves, so that they are at children's eye level.
The one in our village is fairly new but I would assume if it became a problem, a notice would go up. Although an irate post is probably how she feels, she will probably get more luck by posting a polite/friendly reminder that it's a volunteer led service, and asking that people check the capacity of the box before they turn up with a donation, and also asking people to limit their donation to a few books at a time, rather than entire boxes, so that they will all fit in and it doesn't become messy. If she knows of any, she could also suggest other places to donate a larger amount of books. To be frank, some people are a bit thick and won't have thought through that of course a phone box can't accommodate an entire box worth of books from one person. Pointing this out nicely but firmly is more likely to get results than being annoyed about it.
I would also ask in the post if any volunteers are willing to help so that she is not dealing with it all on her own.