Switching from 4 inches to 4.7 inches and then to a 5.7 inches phone, the major difference I have observed is the Travel.
Even after getting used to, a person with an average size of the palm will still struggle to reach out to parts of the screen which are beyond reach. This might require several readjustments of the hand's grip to the phone to reach out the upper half elements in the UI.
A good realization of this can be seen in the mobile market today where entry level phones come in relatively smaller screen sizes along with a flagship phone which is a bigger size. This can be true for iPhone, Nexus and Samsung Galaxy Note series for 2015-16 year.
I see the potential solution to decrease the travel between the UI on the upper half of the screen since naturally the majority of the hand holds the phone from the bottom.
Flipping the Interface might not solve the problem if the device is vertically larger in screen size.
Generally, only a part of the horizontal elements cannot be reached by the thumb of the user. For example, an icon on the left-most side of the UI might not be reachable for a right handed person, and vice versa. So, flipping might only give access to that one icon while the major travel lies between the upper half of the UI from the bottom half.
I would believe a lesser DPI value for Width automatically being applied while using One-Handed Mode could solve the problem of the reach to the icons and elements of the bottom-half UI.
As for the elements that cannot be reached vertically, I believe the current approach, at least on Android is to make the entire screen shift to the bottom right for Right handed users and bottom left for Left handed users. While this isn't the most optimum solution, I think to tackle the vertical travel, the screen estate will need to be minimized for the one-handed mode.
According to the study in 2012, Strategy Analytics in the UK and US amongst current smartphone users shows that more than 90% of consumers seek larger screens than those found on devices they currently own.
Keep in mind, that this was in 2012 where phones were relatively smaller and users didn't mind larger screens which has led us to this point.
The outcome of this study/survey was that Ideal smartphone screen size is 4 - 4.5 inches, study shows. Given that it's been 4 years since the study, one may argue that people might prefer between 5 - 6 inches of screen size due to the rise in mobile entertainment.
A study by the same Analytical company in 2015 suggests that 5.3 inches is the most preferred size by users.
Given this, the current approach on Android in the One-Handed mode strips down the screen size to 4 - 4.5 inches for a 5.5 - 6+ inches phone to either side of user's convenient hand for the one-handed mode.
Another reason why we aren't seeing the screen sizes go up, but the market for them reduce.
One key reason why the screen size of Nexus 6 by Motorola and Google was a failure. It was a 6 inches phone in 2014. The world was barely accustomed to 5.5 - 5.7 inches phone.
We see the feedback take this in due consideration with the releases of the next Nexus phones and their screen size. Nexus 5X - 5.2 inches, Nexus 6P 5.7 inches.
Comparing the study to these phones, it's easy to say that users were satisfied with these screen sizes in 2015. One assumption we can make is, the user's satisfaction of the screen size their phone has is directly related to if they can use the phone with a single hand or not. Given the fact in 2015 the preferred screen size rose to 5.3 inches and anything above alike 5.5 to 6+ inches isn't ideal for one handed use.
Another comparison can be the iPhone. The 6S Plus is easily overshadowed by 6S due to the screen size.
Given these above comparisons in mind, a good solution can be as shown in this video of Huawei's custom Android theme which enables one-handed mode to strip down 1-1.5 inches of the actual screen estate, while shifting the positioning of the navigation icons to right or left depending on the orientation.
A good way of implementation in one handed mode could be to research on the preferred screen size and accordingly strip down the screen to that size and free the other screen estate. This doesn't mean the other estate needs to be wasted really. Designers could make some use of the other estate, keeping in mind to not snatch the user's attention but probably show important notifications out there.