I get more and more of my Amazon stuff via USPS, and it's a good deal, it seems. for all concerned. The USPS has to drive the route anyway, so why not carry something? On our rural route, UPS, FedEx etc can't make money, UPS in particular has a bad attitude as mentioned elsewhere and a high rate of damage to the product. I'm not sure how Amazon actually gets things to the local USPS so fast - clearly they didn't just mail it, as regular mail is never "two day" around here, but I'm getting the stuff on time.
Fedex has been super good from McMaster-Carr, sometimes under 20 hours from mouse click to delivery - in good shape and with good attitude - on *ground* shipping. I also have no clue how they manage that, other than that McMaster has warehouses all over. And they are good the few times Amazon uses them.
But really, in my case nothing beats the USPS these days (wasn't always so, they don't like big stuff) "out here". My mail persons are all nice as can be, know where to leave stuff if I'm not home (will even lock it in one of my cars if it seems valuable), don't get fiddly about details and make me go somewhere (at my further cost) to get what I already paid to have delivered to me. One of my mail people is a retired physicist doing it "for fun" and often drops in just to chat about my physics work. It's another world from what most city folk experience. We'd really hate to lose them "out here".
No way Amazon is making money off me. A small order every few days on prime - if you figure the UPS rates *I'd* pay, prime pays for itself in a month or two. Maybe that's what's driving them.