On the one hand: You need a physical to insure your health. I don't see an issue with insurance companies basing fees on driving habits. Yes, I understand that it'll jack up rates in the long run if it doesn't improve driving habits. But I suspect that people with the box will drive better.
On the other: black-market hacks will show up, allowing people to "prove" they're great drivers. They'll warp the system, making everyone pay more except for them and little old ladies who drive only to church and back. Also, the data would show someone who consistently drives 5 mph below the speed limit to be an excellent driver (no hard acceleration, no braking) even though they actually muck up traffic by driving like morons.
The only solution, as far as I can see, are robot drivers. Nothing else will work.