Interesting concept but I don't think I am a fan.
First of all it is a lot of work and usually for me the books I am trying to get rid of are the ones I don't like so I really don't care where they end up just as long as I can show my hubbie I am not hoarding books. Shh he disagrees with you on that.
Second for you to actually be able to do it with less work you either need to buy the labels, which I don't have the funds for nor do I have a printer to print out free ones. With the Covid-19 the library is shut and in addition to the cheaper prices for printing it is a lot better to do it in black-and-white.
So at this point I will release the one book for BX and see what it does but if it doesn't seem to be a hit I won't be too worried about it.