Customization of UI for single hand use

Looking at some articles written about Apples's new patent on specialised detection circuitry to whether the user is using the phone with their left or right hand, it leads to potential applications of the UI being customized for when you are holding the phone with either hand.

This appears to be a very useful tool to have when doing UI design because of the increasing size of phones and tablets, but perhaps it also causes some friction in terms of having a consistent structure and layout of websites (or apps for users).

Should customisation of UI for left or right hand only usage of mobile devices be simply flipping the interface to the other side (i.e. mirroring as you do for text in languages that are from right-to-left or left-to-right), or should there be certain parts of the UI that stays the same while other parts can be flipped?