We do one delivery from Amazon Fresh per week, more or less (not available in all areas).
Pros: It is awesome to have groceries delivered. We try to meal plan everything out, and then get it all delivered in one day. Works great. We used to try to make one big trip one the weekend, and then maybe one more small trip during the week. But the delivery eliminated the big trip, which freed up a large amount of spare time. Worth it, IMO. I should say also, I'm self-employed, so my spare time is potentially billable, and sometimes I don't have much free time available.
The produce, meat, etc. have been excellent quality. Typically better than Safeway, and well packaged.
It is easy to make/add to a grocery list, and it remembers what you like to buy.
Cons: Stuff costs a little more. Amazon also tends towards higher end products that cost more anyway. Chicken is free range chicken, beef is grass fed beef. Not always, but you get the point, it is a little fancy. We tend to like better meat (and eat less of it), so this is a wash for us, but might not work for everyone.
Non-grocery like paper towels and such don't really seem to be worth it. We get stuff like that at Costco.
In order to get free shipping, you have to buy a decent amount of groceries each month.
But over all, yes for us it is worth it. We save one major chore each week, which frees us up for other stuff. We like it.