So, let’s roll back, way back to the early 1900s when the loop was not some fashion addition, but an actual, functional accessory. You have sailors in the U.S. Navy. They live in cramped quarters on a ship, with no personal space, and no walk-in closets (cloaks?). The uniforms (dress uniforms) needed durability, usage efficiency, and easy stowing and securing in tight quarters. Thus, the loop.
It is referred to as a “locker loop” (or sometimes “backstay loop”), because it allows sailors to hang their uniforms on hooks. Easy as that. Sailors were hanging their shirts, on hooks, not hangers or shelves, just a hook, a peg, and this little loop. So the navy with this incredibly simple design kept their shirts off the deck and wrinkle-free. This goes a long way when you are trying to avoid looking like you fell asleep in your dress uniform.