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.
Sure it’s not perfect. Just like the complaints about self checkout lines at grocery stores.
But there are a LOT of customers who will be pulling out that phone anyway while idle in line - nice if the appropriate app just shows up, and with a few taps is done-and-paid with the order well before the overpaid underperforming clerk is available.
Argue all you like, fact is such apps already exist, and people are already using them to avoid dealing with clerks. All the clerk does is enter the information you can/will with the app; why pay someone $15/hr when most customers would rather do it themselves?