As a couple of commenters have already pointed out – it turns out my idea was “nothing new” (cf Ecclesiastes). Enter the Pocket Canon series:
Pretty much what I described, only using the KJV. And a bit old (published in 1999). Reasonably priced too – 10 for . $24.95 on Amazon
The good news is, obviously there’s a market for this stuff.
Here’s a glowing review from a blog that’s all about Bible design.