This has a number of advantages for privacy (there's no way for the publishers to know how much time you spent reading each story), offline-first availability (dead-tree is the ultimate), and sharing (you can hand someone the entire volume rather than just a link to it, and they get the whole contents, all offline).
It really sounds like it could be the hot new thing, if only some forward-thinking VC would invest in it.
The crux being that it's personalized. It could use my Pocket, RSS reader, reddit/hn voting habits, even my bookmarks db as inspiration. I don't know or care, as long as it manages to deliver me a week's worth every week. Filled with content that I'm going to like 90% of the time, i'd love it and pay for it. I'd even accept ads every few pages.
What I envisioned, is truly slow paced. Like the "old" in depth weekly magazines. Or journals. Something that I have a week to go through, and that doesn't get stale if I don't.
Maybe I should make it myself (though I guess that's my impulsive ADD brain tricking me into yet another hare chase)
Hint: Using a public (book) library also means your reading behavior is tracked by intelligence agencies, unfortunately, so you need to own the books you may want to read.
Although it needs the context to really appreciate the funny.
You joke, but this would be great, and something that every digital solution has failed at replicating so far.
The best we have are newsletters (each from a different site/author) which clutter up my inbox and make me not want to read them. A printed weekly digest of everything (preferably with the comment threads included) would be a great way to spend a weekend.