Why flat design was promoted is different from why Apple or Google redesigned their OSes.

And if you read the iOS HIG, you'll find that Apple doesn't embrace flat design to the extent that people think.

It states upfront that the three main themes of iOS are deference, clarity and depth. Here's what it says about metaphor: "When virtual objects and actions in an app are metaphors for familiar experiences—whether these experiences are rooted in the real world or the digital world—users quickly grasp how to use the app."

It even directly defends skeuomorphism: "GarageBand could have helped people make music without displaying beautiful, realistic instruments, but this would have made the app less intuitive and less enjoyable to use."