Just to add to your observations. For me, several recent Prime deliveries have taken more than two days. And I live in the still fairly dense outskirts of a major metropolitan area, with an Amazon distribution center maybe 10 miles away.
Here in Israel packages take weeks, so I don't have an intuition about this but I'm curious - at what point this fast shipping stops becoming something important, a competitive advantage - 3/2/1 day ? And why ?
IMHO: Predictability is more important than the difference between 2/3 days: if it says "delivery in 2 days", it has to be there in 2 days. If it says 3 days and I need it in 2, then I'll have to find an alternative, but that's better than ordering it, thinking it's going to be there and then it isn't.
1 (next) day is a really nice difference if you need it: e.g. something broke and you want a replacement now, having it the next day is great and saves a trip to the local electronics store.
In the 10 years or whatever I've been using Prime I've never had packages take this long as they have been over the last 6 months. Maybe they are testing out new algorithms?