The only problem with pen and paper as I have seen is it gets stolen, lost in moves, damaged by floods, animals etc. E-logs are good backup for that data especially when you back them offsite. Also some e-logs make filling out all those airlines and insurance apps quick and easy with their reporting systems.
I've misplaced my paper before. But I've also had computers completely crash, and lost USB sticks that had valuable information (pictures) on them. Nothing is perfect. But I like my pen and paper stuff. It's damn near free.