Amazon Logistics works just fine... when they're delivering to an Amazon Locker. I really get the impression that Locker delivery is 90% of what Amazon Logistics was built to achieve (since anything delivered to an Amazon Locker
has to go through Amazon Logistics), and home delivery is just a sideline use-case that they haven't put much optimization work into.
I started getting things delivered to a Locker near my office because delivery to my apartment consistently sucked regardless of carrier (drivers never tried to buzz in; stuff always ended up at the post office or back at the delivery depot.)
Now that I've tried it I'm not going back. Just the fact that I can guarantee where the thing will be (no misdeliveries; no chance of theft from my front door), and pick it up immediately (no waiting in line) at any time of day (since the lockers tend to be street-accessible), makes so much difference.
And that's leaving aside the fact that I've never found anything delivered to a locker to be late (on the last-mile logistics side of things, at least.) In fact, as long as such a shipment enters the country on time, I've found it to arrive faster than its projected delivery time more-often-than-not.
Amazon has a solid experience with Logistics+Locker, but they haven't really marketed it very hard. Kind of surprising, really; the improved delivery experiences might do wonders for their customer retention at a time when fake Marketplace sellers are scaring customers away.