For customers to feel like they're saving time (versus having a cashier take their order) the kiosk isn't it: you can't on average discover and select on a screen faster than you can speak. The time savings of the app/website is from building the order on the way there, reducing the in-store interaction to speaking your name or order number (which is mostly constant across all methods of ordering).
As for app vs website, I agree, website would be similarly good. This could be said about tons of apps.
I don’t know anyone who likes having to order through the apps for fast food places, or regards them as a time-saving convenience—rather, they’re an inconvenience the places make you suffer to get what should be normal menu prices under the broader inflation rate, rather than the 300% markup above that all these places have applied to their menu prices.
Saves having to wait on a line at the drive thru. Or on a line inside the store. Nope, can't do that: they don't take orders at the cashier, so you have to use the kiosks which take even longer.
So I use the app to order while at home, drive to the restaurant and grab my food and leave.
Oh for sure, speaking to a cashier is the quickest/best, and scrolling on a screen (kiosk or app) is slower/worst. I'm just pointing out that if the store will reduce conversations with cashiers by shifting ordering to a screen, then the app is far superior to the kiosk: order before you arrive, avoid germs, frictionless invocation of the loyalty program, etc.
also, there's only so many kiosks available just like there's only so many human staffed registers. This means there's potential for waiting in line. If every one has an app, there's no line. Ever. Well, except for when you show up to pick up your order and have to wait for everyone else.
Of course all of that is just the icing on top of the data harvesting cake
As for app vs website, I agree, website would be similarly good. This could be said about tons of apps.