I wonder whether their subsidizing the app orders to push users over: not just because they can presumably mine other data but because they can hire fewer cashiers and maybe keep their kitchen utilization up if there’s never a delay due to someone slow ahead of you in line. It would not be surprising to see a logical endpoint here treating the cash register like banks treated ATMs where there’s eventually a charge to talk to a person (who might be on video so they can farm it out to a call center?).
Another angle is moving money overseas. A few developers in Ireland subsidiary managing a mobile app which is licensed back to the parent American company and now every $1.00 in profit they siphon into licensing fees is taxed at 12.5% and not 35%.
Every decade or so they bribe US politicians to have a repatriation tax holiday to bring those dollars back home.
Sounds complicated but another likely reason they want you to use their app.
I suspect its more about market segmentation. Its a slight hassle to use the app and if you want those great deals you dont get much choice in what you can order at a discount - the discounted menu items rotate frequently.
So people who have more disposable income wont make a habit of using the steep in-app discounts and just order whatever they feel like eating at MSRP.