Thank you Stefan.
I have informed me about the functionality of the display first (and missed to search for existing discussions on my suggestions) and tried to implement this in my idea.
I am a user with limited experience, so my list of cases the phone needs to withstand is maybe incomplete.
First case, the phone falls from a usual hight, the drop would be absorbed by the whole cover. With a well calculated width of the wooden wall framing the glas, the shock would be - instead of passing directly to the fragile corner of the glass - absorbed by the cover. Oak and a fiber direction related to the corners, to overcome the shear stress, could make it possible. Additionally the display could be stabilised by the core module, and connected to the cover by flexible parts.
The rim instead uses the flexibility of the material and slows the drop by stretching as well as taking the shock from the fragile glas corner.
Second case, scratches from inside the pocket. The rim protects from long items like single keys. A bunch of keys or round and small objects would have the same impact on both constructions.
There also could be found some space to implement magnets, allowing a flip cover on the front. Making this cover from well traded leather, and the wearing part gets even more beautiful with the time.
Third case, the phone has been laid screen first onto the table. Here a rim has the most advantage.
Are there many people doing this? I wouldn’t do so.
By initially writing this contribution I focussed on the first case. I would like to hear if I missed some cases.