Insurance companies offer this in some countries.

I'm in a driving study right now that installed a black box (plus a couple of cameras) in my car, to see how people drive. The study took care to make sure that the recorded footage and sensor data can't be accessed during any incident; it's encrypted, they resist requests from the police, etc.

In a related note, I can't cross US borders until the driving study is over; the border police are Not Amused at being recorded, and the researchers really discourage trying to cross a US border in the car that the gear is installed in.

There are already discount programs for people willing to install monitors in their cars (Progressive Snapshop, among others).