File managers may be out, but photo apps might be OK: they just need to somehow request full access to /DCIM through this new API (which I have not looked at). music & video players may be more awkward but possibly doable.
So moving from Android to iOS will be less painful in the near future. I think traversing the whole filesystem and adding a big SD Card are key features in Android devices.
If Apple launches a device with a bigger display they will eat part of the Android ecosystem.