The reason that statues don't have eyes or pupils is really just a matter of style and a preference for how to deal with a problem.

Artists have developed many different ways to deal with the depiction of the eye.  The problem is that there is no way to sculpt the eye as it really is.  A real pupil is actually a hole, of course, but it is covered by the cornea. So we see the black shadow within the pupil, but the physical shape of the eye is a closed orb, because of the cornea. It impossible for an artist to depict that, so an artist has to make a choice in regards to how to portray the eye.  

Some artists will actually carve into the orb so that natural light creates the illusion of a pupil; when a shadow fills a physical hole it looks like a pupil.  Other artists prefer to build the orb as it would exist physically and leave it up to the viewer to infer or imagine the pupil.  It is all just a matter of preference. Different periods and regions had techniques which were more or less popular, but ultimately it has always been about an artist's preferred means of dealing with this problem.