Pressing both side buttons has nothing to do with driving.
Now, it would be possible to use the same mechanism they use for digital drivers licenses to further restrict it but the nice thing about that idea is that not using sensitive information means there isn’t much concern of a leak.
Have you actually seen what amazing technologies are worthy of the name "privacy-preserving" these days? You can look up items in a database without the database operator knowing what you queried. You can let a server add two numbers without the server operator knowing what these two numbers are. These are worthy of the phrase "privacy-preserving" in this age.