Replying to myself here: I suspect one of the reasons Amazon uses a multi-tiered approach to shipping is because it allows them to keep personnel costs lower. Instead of hiring enough people to handle high-volume days, they employ enough staff to handle the average volume and then use low-priority customers as a buffer to "catch up" when a surge occurs. High-priority customers always receive shipments on schedule, even during a surge, and the low-priority customers can't reasonably complain about the terms they agreed to.
Slower shipments certainly encourage people to upgrade, but that's not the reason they're slow. Free shipping is still a big selling point for a lot of customers, and Amazon's approach is just one cost-efficient way of satisfying that demand.