I'd prefer something with a slightly more libertarian bent:
The hardware is required in new cars. It's illegal to make it report false values or for someone other than the driver to record. When you press the start button, an LED shines into your skin and records fingerprint hash, and blood alcohol. This data is recorded/reported only when a public road has been entered or crossed, and erased from local storage in 24 hours.
The reporting is optional. You can turn it off. You set it up to report to your insurance company. If you don't, your insurance rates will probably rise.
What does society get out of this? People are strongly encouraged not to drink and drive. They get a clear and unambiguous signal if they are over the legal limit or not. We get some insurance data about how many people are drinking and driving nonetheless, and their actual accident rates. Insurance rates can be higher for people at higher risk, and lower for those who are not. There's no emergency situation where someone can't activate their car. Drivers' "freedom" to drive without insurance or without historical monitoring isn't infringed. You can still drive drunk on private property without consequence.
We could probably also partially do away with constructive DUI (DUI where you are drunk, but asleep in the vehicle and in possession of the keys). You can set a maximum startup BAC in the car computer. You can lower it, effective in 8 hours. Your sober self can agree that future you shouldn't drive drunk, and even if you sleep in your car, the police can't show that you were in control of the vehicle.