Thank you very much guys for your comments and feedback. I just wanted to say that after messing around with it, I have downloaded Maya 2016 LT (15 days trial) and decided to try its new UV tools.....
The result - Oh my God!!! Honestly, I took my case mesh inside and made camera projection from top view then opened the new UV editor and pressed "Optimize" and it relaxed the mesh in 1 click absolutely automatic without almost any curvature. Took a few minutes to fix some bends but that is all, it was so easy with new UV Lattice / Smooth tools.
Anyway, in my opinion - Maya 2016 LT's UV tools are the best ones I have tried yet! (and of course full version as well when it comes out, guess its gonna have the same toolset)
EDIT: Added a preview of the interface and a preview of an automatic relax mesh (it is another phone case for Galaxy Note 4 with even more cuts) .. just so you can see how clear it comes out with that complex mesh. It is amazing! No cuts, no seams, nothing - just plain projection then relax. It is even more beautiful with simple models.
LOVING the new UI as well ;) - I made screenshot with smaller window so it doesn't take much space in the post. I work in 1440p normally and it does look stunning!
@maru - when you subdivide there is an option for UV subdivision as well, if you click edge only the map will be left intact just like on non-subd'd mesh.