I have bought a couple rechargeable LED lights to use for reading paperback books in bed and always had issues with them staying on the book, shorting out, battery not holding a charge etc. As other pointed out, a standard case at 35$ and then even an inexpensive booklight puts you close to the cost of the lighted case. My thought process is this wouldn't be something I would lose or not have at hand when I wanted it since it was built into the case. I also assumed that since it was a first-party accessory Amazon would have done some good R&D to make sure it worked well with the device.
I could of course be totally wrong when it arrives but the 30 day return window will let me judge it at little risk.