Earlier quoted context omitted.
This button isn't about saving time, it's about preventing the instances of not having something when you need it. The moment when you realize you need more of something is typically when you're using it. If you can literally just hit a button to order more, that's a significant change from having to do something else to order more.
My problem is with some items that I buy only twice a month, like bath soap or mayonnaise. I notice that it's about get empty (or it's already empty :() and I put them in my mental to-buy list. If I'm lucky I'll remember them the next time that I go to the supermarket. And probably also the following time and a few more times until I realize that I got a lot of it and I remove the item from the list. So I don't have…
Another good use case is that I can head to the store as soon as I realize we're out of something, and by the time I get there, the list has everything else that she thought of.