The app does detect when you are going over a certain speed and flashes up a warning that only allows you to continue if you are a passenger.
However, as the game is designed for those on foot, it would be reasonable to disable interaction with the game whilst travelling above a certain speed.
There is a legitimate reason to allow the game to function without interaction as pokemon 'appear' in certain areas and the app radar will identify them when in range. If you have to stop moving to interact this would be safer than the current system. It would also allow a passenger to tell the driver to stop in order to catch a pokemon...unless the player was on a train where the request might cause offence.