It depends on the artist, and whom the artist wants to communicate with. Some artists create for themselves and don't care what the audience thinks. They label the work "Untitled," and say things like, "The piece speaks for itself." Some artists create with other artists or the art crowd as their intended audience; if the broader public gets it, all well and good. Some artists want to reach everyone. (And the funny thing is, you might work with a particular audience in mind and reach someone entirely different.)
It's not really a structureless medium (media), though. The structures are there. That most people don't learn enough to see them is largely the fault of Art Fear in public education. Or so I declare.
P.S. - Bald Eagle, can your son transfer to another school? Different schools have different philosophies.