The aircraft have to have current documents on board. It is a legal requirement.
I guess the simplest way to draw an analogy is your car tax disk. You must have a valid one on display on your car window. It's no good having it at home. The Police will question you if they pull you over. The same thing with aircraft. If you're Ramp checked by the local Authority, eg CAA and you don't have the current documentation on board the least is a Non Compliance Notice, the worst, the aircraft is grounded until the valid documentation can be produced.