Strong lats stabilize the back (and assist in stabilizing the scapulae) and transfer force from the lower body to the shoulders/arms. If you can't squeeze your lats during a bench press, then you won't get any leg drive. Big bench presses rely on leg drive, as do big squats and deadlifts.
Eric Cressey goes into more detail on the subject in this article:
Lats: Not Just for Pulldowns!