Polygons and why we like them

I think the confusion with "Oh no, not polygons" is that polygons, unless they are elevated to an art form, as in the preceding music video, can be a really crude way of creating something. For example, this does not look much like an apple:

Many CAD systems do have other representations such as Non-Uniform Rational B-Spline (NURBS), which is a type of curve, or primitives that essentially have no polygons but are what they represent. A sphere, for example, may be arbitrarily smooth with no facets or flat areas.

The world would be boring if everything was just cubes and spheres. Unless it was Minecraft, then it would be pretty cool. Aside from Minecraft, many CAD systems build up more interesting objects via Constructive Solid Geometry (CSG) to drill out and add the basic primitives to other primitives to make more complex objects. 

Why doesn't VR use some of these techniques?

Generally speaking, they are slow. Something has to convert the precise, accurate mathematical...