After using iOS 7 for a few days, I think I get it now, and how the radical re-design fits with the company's business objectives:
There are fewer visual affordances
Yes, 'Find my Friends' leather stitching took skeuomorphism too far, but at least buttons used to look obviously 'tappable' across iOS 6. In iOS 7, some text is tappable, some isn't. There's a steeper learning curve and greater cognitive overhead in working out how to use most of the built-in apps.
More functionality is hidden
Fewer 'grips' to slide things open, a hidden 'Control centre', pull down to expose search on the Home screen, the 'swipe back' gesture - and so on. These are, Apple assumes, power-user touches - and power-users will happily learn how to do this stuff.
The user interface throughout is smooth, slick and responsive - the transitions in particular feel classy, and the realtime 'frosted glass' effect works really well.
Put this 'premium' feel together with more 'expert level' functions and the high-end iPhone 5S hardware (plus a cheaper model at a lower price-point) and I think the result is:
Apple isn't trying to make a smartphone for everyone anymore.
Any electronics co can churn out cheap Android devices and compete in a messy commoditised space it figures, meanwhile the high-end is Apple's to own.