advantages of head lifting in benching

I've seen a lot of people lift their head while benching. What advantage does this give the lifter?

Any disadvantages?

I've heard it can decrease range of motion, but when I try it, it doesn't seem to make a difference. I also heard it can help push the weight up when putting the head back down, again I haven't been able to experience that.

Lifting the head up at the bottom during the bench press is used by lifters using a multiply bench shirt in federations which allow this kind of technique. (IPF and other raw and single ply equipment Feds usually are stricter).
The technique is called Collapsing.
When a bencher pinches his shoulder blades and sets up with an arched position, he is stretching the chest plate of the shirt.  Once he starts lowering the bar,the shirt quickly loads to an extent that it is usually impossible to stretch the shirt further and touch the bar to the sternum while keeping archedosition and retracted shoulder blades.  (Provided the shirt is not oversized).  So at that point the lifter collapses momentarily by loosing his arch and flattening his chest, and in doing so he puts his head forward.  This releases tension in the shirt and gets the bar to touch.  On the press command the lifter pushes the bar upwards and quickly gets back into arched position again to lock the bar out with retracted shoulder blades firmly pinned against the bench.