The iPhone Air seems to have split iPhone mini fans into two camps — those like me who mostly care about pocketability and those who want a small iPhone. I racked up 10+ miles of walking over the past two days and barely felt the iPhone Air in my front pocket. It's less noticeable than the iPhone mini. Thinness matters more than dimensions (provided the iPhone Air fits in your pocket, which it does).
Also noteworthy, I was able to use the iPhone Air in bright sunlight wearing sunglasses. I always had to raise my sunglasses to see the iPhone mini display. With so much attention on the single camera, single speaker, etc., it's easy to forget the importance of the display, memory, and processor — until you actually use the iPhone Air and realize how much better the user experience is versus a 4-5 year old iPhone. The single camera is likewise a significant upgrade over the dual cameras on the iPhone mini in terms of quality.
It'll be interesting to see what iPhone mini holdouts eventually do. Given that Apple solved pocketability with the iPhone Air, it seems unlikely we'll see an iPhone with a display below 6.1 inches ever again. Instead, the "e" model will likely increase to 6.3 inches at some point.
I don't think the iPhone Air will be orphaned as some have posited. The thin design is clearly the future and Apple doesn't casually give products the "Air" brand. Instead, I suspect Apple wants to eliminate all version numbers on iPhone models as it did with iPads after the "3." As for the iPhone Air (Second Generation), I'd be happy with the A20 Pro, 16 GB of RAM, and whatever main camera the Pro models get.
Thinness not solve the overall size issue that all the latest phone have.