As an EEE student myself who's also interested in renewables this is interesting and you make a good point but A, bezels are only ever shrinking to the point where there won't be a bezel any longer and B, the most efficient PV cells are at best 20% efficient in bright sunlight and where I live that isn't very often. I think better tech would be using power from kinetic oscillations like walking or from thermal energy like body heat, this could contribute to an extended battery life.
I'm actually ok with the bezels if they have some kind of "hidden" technology in them, but yes, you're right about that.
That's one of the solar energy problems. Some countries have very few equivalent hours of full sun which can be seen as a problem. This kind of device will only be efficient on 40% of the Earth's surface. Considering that nobody lives at the open sea, it will go to around 20% or less. If this would actually be used to power the backlight as someone said above, it could work but not as a "backup battery". Thermal would also have problems attached to it because the average temp. of the human body is not enough to be efficient as well. About kinetics, I'm not that comfortable talking about it