In my car (BMW from 2012), the engine does not shut off when you press the start/stop button when you're driving. It only shuts off the engine when you press it AND you're stationary. This seems like a totally obvious interlock to me, it puzzles me that Ford didn't think of this and as a solution moved the button instead.

Does that button really start and stop the engine? In other cars I've seen, the start/stop button (with similar iconography) toggles the start/stop system, which shuts off the engine when the car is stationary to avoid pollution.