When I moved to a place that had this wond'rous delivery invention, I decided to try it out. This is what I discovered:
1) I am too cheap to make the most effective use of this, which would be to have fresh foods delivered every few days or so. Since I hate grocery shopping, I only go once every week or two, which means most of my foods are frozen or non-perishible. It would be nice to have fresh fruits/vegetables/meats delivered to me as I eat them, but for some reason I can't justify the delivery charge on such a rapidly-recurring basis.
2) Fruits, vegetables, and deli items are very difficult to buy sight-unseen. Sure, they will be picked out for me by a human, but I don't trust someone making $8.50 an hour to find me ripe but not overripe bananas or "some roast beef unless it looks like it's been out a while." You also can't say "Some seeded kaiser rolls, but if they don't have those get wheat ones if they aren't too stale."
3) I always miss something I need, because I'm not physically browsing the aisles and being reminded of them.
4) When trying new items I will often buy the wrong size, because I didn't have the packages in front of me.
5) It is very hard for me to remember exact brand names and packaging sizes of things I like, which makes it difficult to search for them online. The result is that a purchase that takes under 2 seconds in the store takes several minutes of searching, refreshing, and reading online to make sure I get the size/item I want.
Basically it was a neat idea, but it didn't work well enough for me to continue doing it. Plus they opened a grocery store like 200 yards from my apartment and I'm not paying $10 for someone to drive them up the hill in a truck. What I might pay for would be to have a fresh, guaranteed healthy meal delivered every day, but my inherent cheapness would probably torpedo that, too.