Perhaps you have never been stopped by the police, or encountered a random DUI checkpoint, but I can assure you the Constitution is not high on the list of priorities for the officers. Leaning inside the car, looking everywhere they can, sniffing around, asking you to get out, shining lights in your face and inside the car all are forms of search. And of course, if the officer claims he "thinks he smells something," they will open everything and do a full search. And NO, I have never been arrested or accused of DUI, open container or any other illicit substance crime. That's the point, they are doing all this with NO probable cause.
If you'd like a better argument, here it is:
It's not Apple's place to enforce laws (drunk driving or otherwise.) If the government tried to pass legislation outlawing this type of app, it would probably be found unconstitutional. It's much easier for them to just get corporations to go along with their suppression of free speech, then they avoid those nasty constitutional challenges. That's why AT&T and other communications corporations willingly give access to their customers' cell phone and email communications to the government (in the interest of "national security," "the war an terror," or some other dubious justification.)
Even if you object to THIS particular app, you should be more concerned about Apple's willingness to be a government proxy. Their response should have been, "Show us a court order to remove the app, then we'll do it."