The back and face frame stabilizes significantly shouldn't be an issue. The bottom rail and back will support the bottom shelf.
I agree 3/4 ply is sturdy, but not as much as you think. IME shelves >30" loaded with books will sag if unsupported. If you're doubting this take a piece of 3/4 ply 12" X 48 just supported at the ends, put a 10# weight in the middle and check it 24 hrs later & see if its sagged. Now imagine 40# of books on it 3 months later.
On shelves, I like to apply a 1 1/8 X 1 edge strip to the front edges with a 3/4" X 3/4 rabbet and chamfer the edge back to the glue line. It may seem like overkill but I think its worth the extra effort and on a shelf >30"loaded with books, it will never sag. If the shelf is wider than 30" I'll add second strip to the back edge similar to the front.
You've got to address the edge anyway, why not do it?
Last edited by DrRobert; 12-04-2019 at 02:45 PM.