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.
The feature described would be a nice way to support those questions in a manner which does not reveal private information, require you to unlock the phone, or otherwise risk giving them access beyond what’s needed to answer the questions during an official investigation. You could of course choose not to use it but why you’d want to give them additional access to your device is beyond me.
Even the breathalyzer requirement seems irrelevant, considering that it only requires you to submit to a breathalyzer performed by a police officer, rather than mandating that your BAC be available to anybody with physical access to your property.
You can’t answer their question with anything but hearsay. This is why I brought up the DUI checks because we know some people are going to lie, and hard evidence can easily be acquired to sidestep that issue. The suggestion above would be similar in terms of having minimal privacy concern and because it’s cheap and easy it’d actually be done in non-egregious cases.
I also reject the comparison to DUI checks on the basis that those must be performed ASAP in order not to lose the evidence, thus necessitating urgency; the same doesn't apply to phones. As we've seen in, for example, the case of the Uber self-driving car operator who was using her phone when she killed a pedestrian, they were easily able to determine this after the fact, without such intrusive features.