This is a great idea. Why hasn't any one done this before?
I'm guessing it's because exposing batteries to direct sunlight isn't a safe thing to do. Additionally, it might reduce the recharge capacity by affecting the components inside.
I think that you would have a tough time charging batteries like this, primarily because a cylindrical surface will have very little direct (normal to its surface) sunlight. Most of your solar cell surface seems to be either in the shadow, or at a pretty weak angle. It would be far more effective to have a foldable umbrella like thing that you open up and point at the sun.