There have been some successful drone cases (distributing medical supplies to rural hospitals), but those were fixed wing and had some creative launch and "landing" systems and the payload was parashooted down.
When I look at the 'quad' delivery drones like for Amazon, I see a functional issue. High density locations, don't currently have a good way for drones to land (so anything were individuals don't have their own yard/landing area for the drone), so this takes out [big] cities.. at least currently, even though the population density would be ideal for something like this, given the range of the drones.
Without going to fixed wing flight, there is a range limit on the drones, which limits more rural areas (which again there could be some value here if not for range limitations) even though there could be some potential value here in saving costs for drivers to drive trucks to the various locations.
At some level, I think this is mostly in R&D, even being willing to operate it as a loss, for the hope of having tech in place for if/when something changes to remove one or more of the current barriers (better battery tech would be a huge change here, so would installing 'delivery docks' on high rise buildings).
I don't think there is any plan for this to replace 'normal' delivery stuff that many/most people see, however there are places were Amazon has 2 hour delivery for some items, and I think this is the situation that the drone delivery 'market' may be targeting right now. The ability to "instantly" dispatch a direct to end point shipment over an area could make it so amazon could compete with Brick and morter stores for more things. think about running to the store for something small vs paying an extra $1 to have it delivered for you in under 1 hour... that may very well be the market that something like this impacts in the near future. (were I am at, that would probably _save_ me money as the nearest store is 10-15 minutes away at 55 or 65 mph, so I am very likely to have spent $1-2 in gas to do it... then there is my time also).