The head off bench is also popular with shirted benchers, it helps with adjusting the groove for touching the bar to chest in a shirt.
On the flipside, in addition to what the other video mentioned here, a reflex called Tonic Neck Reflex usually happens when driving the head into the bench, which helps with drive and lock out. A master at this was Doug Young, if you watch his old bench press videos, he keeps his head position very softly on the bench during the decent, on the upward drive you see him really bear down sometimes.
I've always been a neutral head position, flat back guy myself. I find it the most comfortable for normal day in, day out lifting.