“Is there some Apple app out there that has even .001% of the country’s restaurants’ menus on it?”
Consider relevant precedents:
Facebook.
Twitter.
Google.
Yelp.
Amazon.
...and others.
Those services didn’t exist not long ago; today, they DOMINATE their sphere, knowing “everything”. Google went from nothing to a near-complete cross-reference of _every_word_ on the Internet. Facebook has 10% of the _world’s_ population as members. Twitter is huge. Amazon handles around 1% of USA retail sales. Yelp is huge. Etc. And each one has its own app...and is becoming integrated into the umbrella called iOS.
A great many restaurants already have their own apps, menus on line, allowing you to order & pay. If Apple doesn’t build such a service right alongside Pay itself, _some_ app will arise as the dominant aggregator of menus, notifying you upon arrival at a restaurant, showing the current menu, letting you choose, and handling the payment with just a finger touch. It’s just too darned easy, and profitable, and timely, to not happen.
That's a fantasy. There's too much clerical work involved in keeping Apple's menu database up to date, especially since there's nothing in it for the restaurant. Many restaurants have daily specials, which would need to be input each day. Some restaurants sometimes run out of something, so that would have to be told to the app as it occurs.
When I dine out I don't order everything right away... I need to see how it goes before deciding on a dessert. I also can't predict if I'll have a second glass of wine or not.
How does what I order on the app get communicated to the waiter? How does my order get entered into the restaurant's pos system so they can total out (Apple app orders and all the other customers) at the end of the day?
What if something I order turns out bad and I send it back... does the waiter have some sort of override code where he can get into my app and change my original order?