They already did this in the UK about 6 months ago, replacing the existing couriers with Amazon Logistics. Which incidentally, is a plain white van, here anyway.
Where before you could track your package and get told within an hour when it'd turn up and get regular updates (unless it was a cheap item which they sent via Royal Mail), now you're told on the day that it's out for delivery and that's the extent of the "tracking". It can turn up any time that day. Be careful what you wish for, as I find this a step backwards. They're also more strict in my experience - if you get something like a mobile phone, they insist that YOU are there in person with ID. So that means you have to get a day off work to wait for it and can't just have your family member who's already at home receive it, or if you get it delivered to work they have to track you down (so in places like mine where you could be anywhere in the factory and they have to wait for you to respond to a call out, they'll be less inclined to continue allowing personal deliveries)
I can only go by the UK version of course, the US policies and systems could be completely different.
On the plus side, you tend to know audibly when your package has turned up. Obviously a carrier is a carrier, they all do much the same thing, but there is something unique about the exact noise of the sliding van door, the amount of time they seem to need to rummage around looking for your package, and the "bleep!" of the barcode scan they do just before they ring the bell. It wouldn't surprise me if they trademarked the "Amazon Delivery Noise Pattern" :)