I do like the idea and have seen a couple neighborhood mini-libraries similar to this (they weren't in retired phone booths though). The thing I'm not sure of is exactly how much use I would make of one were it near me. Nor how likely I would be to lend books through the "system."
I think the honor system would work well for the most part. Here in Denmark -where I am staying at present- the public transport uses the honor system to some extent except for the times when there are ticket checks (not often in my multi-week experience). There are also many "gårdbutiks" - small garden stalls or shops where you can purchase produce, flowers and eggs. Payment is by leaving cash or using the MobilePay app linked to your bank account. Again I hesitate somewhat to call this the honor system since I've seen cameras recording the gårdbutiks. It's a sort of "trust but verify" system perhaps.
I've experienced the same system in place at historical sites I've visited as well.
Potential issues I see with the mini-lending library (despite the fact that I like the idea) are:
- Tragedy of the Commons issue as described by @onceuponatime
- Would there be quality books I would want to read? (already a problem sometimes with small traditional libraries
- Would I be willing to share my books?
- Borrower forgetfulness (books checked out for long periods and eventually lost)
You make a lot of useful observations. I don't think that the idea is to put the book back but to have the books circulate with people putting in other books!