I need to add a couple of electrical circuits that will run across the floor
joists of an attic. The attic is accessible, but it has a low ceiling
height, so the attic is not (and never will be) a usable living space.
There is no floor in the attic space -- just the open joists which are the
ceiling joists for the rooms below.

Since the new circuits will be running across (perpendicular to) the open
joists, is it okay to just run a nailing board across the top of the joists
and staple the new wiring on top of the nailing board? That would be a lot
easier to do than drilling through the joists and running the wires through
the drilled holes.

Is the nailing board approach okay according to the NEC requirements?