My 2c is pretty much echoing what more experienced pilots have said. Camera's are a distraction, and you don't need distractions when you are trying to learn in an expensive learning environment. I'd suggest that the ability to go over things on the ground would cancel out what you'd be learning in the air, and it's in the air where you want to be learning at your optimal rate. I kept a diary of my lessons by brain dumping after I got home, and I managed to glean quite a lot just from my recollections. Even after getting my license I don't generally film myself, I take a friend along who does all the filming so I can concentrate on "Aviate, Navigate and Communicate".
Just my opinion.