I think it could depend on the protections Google (and Apple) puts on this type of thing.

You could imagine a scenario where putting a phone into driver's license mode disables Face Unlock, and maybe even pauses all push notifications like text messages, and therefore is more secure because it forces people to put their phone into a password mode. So it'd actually encourage people, when talking to law enforcement, to increase their security settings.

I don't know if these companies currently do it like this, but they should.