I have a commission to make some wall-to-wall hanging bookshelves roughly 45 inches tall spanning 137 inches. I will make these as face frame cabinets in 5 pieces, with the longest span appx. 37 inches. So far, so good. I had considered hanging these with French cleats but then it occurred to me that after routing a rabbet for a 1/2 inch cleat and a 1/4 inch back, the top of the case might not be stong enough to hold the weight of the cases and the books. The rabbet would be 3/4 inch deep and 1/4 wide, leaving essentially 1/2 inch ply holding the entire weight of the cabinet and books. I suppose it would be possible to rout only a 1/4 inch groove and trap the back, but then I'd still have only 1/2 inches of ply at the location of the groove.
Is this strong enough, in your experience, or should I go back to a stretcher between the sides on the inside of the back, much as most kitchen cabinets are mounted?