Having been at a very low level of this I can confirm the daily reviews. And yes it is extremely effective, if you have the right people.
The delivery time thing is, IMHO, ober simplified. Not sure if Clark is reviewing that life, but it is reviewed for the previous day. At least on the warehousing side of things, lead times are closely watched as these directly impact promised delivery dates for everything stored there. Same goes for transportation lead times. The worst thong to happen is the "red button", if that is pushed a complete warehouse looses the Prime status, meaning only standard delivery is enabled. Happens quite regularly so, and I even remember a Big Red Button when the whole network was affected. It just shouldn't be to long.
The most important metric at my level was missed shipments. More explicitly shipments missed due to the warehouses fault (ready to ship on time but not picked up by the carrier). Even worse, shipments that missed the promised delivery date. It speaks volumes about Amazon's logistics systems that all this could be figured out before 9 o'clock in the morning for the previous day. And it is one reason why you learn so much there.
Regarding people, Clarks ability to manage the network not only depends on the low level guys (like me back the day) but also managers in between. If these managers got their priorities right the system is less harsh then one might think. If managers play politics, not so much.