It gives more confidence in the service at the time I'm thinking about the order. I want it to be reliable so I don't need to track and worry about it.

Precisely - Amazon is the one retailer I literally delete order emails from.

Basically everyone else I keep the latest status mail (ordered / shipped / arriving tomorrow) in my inbox because they have not earned my trust, and orders have fallen through the cracks before.

Anecdotally Amazon is 90% of my online shopping (by order volume) but only 10% of my unshipped/wrong item/misdirected/lost packages. I have had mis-delivered packages from USPS/UPS/FedEx even on large/high value items.