Sure. I wouldn't mandate it. There would be no incentive to mandate it, when the owner remains in legal, practical control all the time, even in court.

I think most of us would still use it. To record our lives so you can review or share the good parts or prove something you said, heard or seen. It's already happening with phones (they just don't record all the time but that's mostly to technical limitations) and I think people today would love to be able to get easy, legal access to footage containing them from other sources.