I made this design from Matthias Wandel a few years back, and it has served me well. I had a big piece of laminated MDF that someone left in the garage after we bought our house -- perfect for the top. I do with that I had something heavier for when I need to whack a chisel or do some ripping with a handsaw, though.
Yea, the aprons make it really robust, but that lateral stress on such a small area seems like it would flex. I'd either want that stretcher or some cross bracing at the rear.
If you don't expect to move it, you can cheat and drive a single lag through the apron into a stud. Then it'll never move, for sure.
Though I admit I'm impressed it doesn't already flex, what a beast!