A form of barrier against the elements, walls provide secure detachment from the world. It ensures direct separation from the inside and the outside. It is not, perse, a wall if you place an opening, or a door, or a window; in this way, the definite line between inside and outside is blurred.
As a support structure, it is not much of one. It does not carry any load, except for itself. To make a wall support anything other than itself, beams and posts are added. With these additions in place, it cannot be a wall anymore, since the lateral force needed to bring a wall down is different with support structures embedded in it.
As a form of trial, walls are used to block troops from coming in. These walls are fortified to withstand any incoming attacks. If the wall falls down or falls apart, it cannot be considered a wall anymore. It will have lost it defining characteristic as a blockade or protection.
To climb up a wall brings no shame to the identitiy of the wall. It is, by far, the gratest way to overcome this wall, without removing the defining characteristics of the wall itself. With the act of climbing, it still provides a barrier, since itstill blocks, fully, the inside from the outside. In climbing, also, no purpose is executed to support anything else, not even the climber, thus the wall remains to be as that. Also, it still provides a challenge to the climber as it is strenuous to scale up and down the vertical face of the wall.
They say, in fact, that "people build walls, so that they can see those who care enough to climb them".
