Last month I had to go to store at least twice in the morning before work because we ran out of milk and my two year old was close to having mental breakdown without cereals for breakfast. We use combination of Google Shopping Express, Walmart and Safeway delivery services - they are godsend and save us enormous amount of time. Unfortunately Amazon Fresh is not available where we live.
Having one second ordering for regular staples will marketdly improve ordering process, especially if buttons are reliable and convinient to use.
It's definitely a common thing for me and my fiancee - we're not forgetful people, just busy. The less disruptions and banal activity in my life the better.
Why not order it on your phone at the moment you notice that you're running low? You can do that right now, without a special Amazon button.