Thought I'd tag my opposing anecdotal data point onto your comment.. I live in London. I've had maybe 50 next day Prime deliveries in the last year - none of which have been late, lost or other.
Here in Tampa, the "standard" next day delivery services (where there usually is a surcharge) is fine (using the standard Fed Ex or UPS option), and I've never had a problem with the standard 2 day Prime service delivered via USPS or the like.
However, for some products, Amazon offers a "free next day delivery" service option. These services tend to be offloaded on sketchy "courier service" companies with names like A1 Courier Services, Lasership, Ontrac, Dynamex, etc. These carriers get generally awful reviews (as seen here: http://www.amazon.com/forum/amazon%20carrier%20feedback/) and you hear a lot of reports of missing packages, late deliveries, etc. I've only used this option once, the item did arrive, but it was at quite a late hour (10PM). Based on the reviews, I would not use this service again.
I still use Amazon a lot, but they have become way sketchier over time. Knockoff batteries are but one symptom of this.
It was indeed one of these sketchy courier services. They dumped my package by the front door of our apartment building at 10pm on a Saturday night in NYC. Or they claim to have. An hour later when I got home it was nowhere to be seen. I waited home most of the day for it until I had to go out to a previous engagement, too. The previous time I had a next day delivery, they claimed to have attempted delivery mid-evening while I was at home but never even rang the bell.
They are very good at logistics for me!