Although nicely executed, I really don't see Dash being more than something a gadget freak uses for a few weeks and then sits in a drawer forever. Also doesn't help that the area for Amazon Fresh is so small too.
In fairness however, my wife and I use grocery lists on our phones all the time (though it's only two steps, not the OP's 7: (1) "put peaches on my grocery list" (2) confirm).
And then possibly a text message. Of course, it goes from being 2 things to 10 things quickly. And then I'd have to deal with actually keeping the list orderly and constantly checking what I did have in the basket already (more difficult with 20+ items).
So, I wrote an app. It was funny, building a "twodo" app. But honestly, I just needed something that worked.
I mention all of this because it did start with trying to use what we already had.
"Number of steps to scan grocery by phone"
Most people just use pencil + paper, or notepad/note app on phone. Never have I seen people actually use technology while shopping unless it's a typed out list.