I worry that the interests of car companies and government are well-aligned here and any regulation will be in the direction of making logging of everything mandatory for the benefit of law enforcement.
Meanwhile, no need to have the data leave the car "for the benefit of law enforcement". I would love if cars' would be GPS connected, or use "smart roads", and have the car self-regulate the speed limit. We have the technology to get rid of speeding tickets, lets just automate this and lets debate better road policies instead.
No need to reduce the number of police officers, just get them to instead work on finding my stolen bike! They can also continue to patrol the roads for unsafe driving, for people who mod their cars to no longer respect the speed limit, etc.