It’s a whole lot easier than you think it is. Actually, I may suggest it to our sales guys (base infrastructure & app already in place).
You’re also off track: the threads intent was fast-food type menus, where the offerings are stable & national, and clerks are just filling checklists and processing payments.
Even if it's limited to fast-food joints, I see hassles and no benefits to either the customer or the establishment.
It would be much easier for me to walk up to counter and say "cheeseburger, small fries and a coke" than it would be to pull out my iPhone, fire up the menu app and locate the items on that tiny screen and place my order that way.
If you walk in and order things, including a strawberry milkshake, and then learn they just ran out of strawberry milkshake stuff. Does the clerk have some way to modify the order on your app, and if so does that mean that clerk will now need to learn both the regular POS system the place uses AND the system which allows him to modify Apple Menu App generated orders.
There's no real benefit for the customer, and the operator of the establishment would have increased cost of operation to implement and use such a system alongside their regular POS system.