I am newly qualified - so defer to all the more experienced, but anyway.
First few months I asked the instructor to take the occasional pic of me/the countryside so I could show friends and change my work background - I wanted to record everything. Reality is there is zero to be gained from filming the beginning of the course - turning, straight and level etc. Zero. It took me a while to get the flare just right - again, not something you can usefully "fly" on a video.
What could be helpful - stall/spin recovery. You need to take particular actions in quick succession that need to be learned. Less finesse on the inputs like small adjustments to fly straight and level and more bang pitch, bang power and bang climb. Also I think PFLs - again, a succession of actions to learn - pitch for climb etc. I think IF you struggled with these for a couple of weeks you could legitimately ask your instructor to fit a camera.
So my advice is don't waste the mental energy in trying to film hours of boring nonsense BUT when you get to specific points that you struggle with I can certainly see the benefit of 5-10 second videos (longer for PFL) to re-enforce what needs to become muscle memory. And there is nothing wrong with asking for the occasional landscape or you pic - learning to fly is cool and fun and so I can understand why one would want to record it!