You're looking at points on a continuum as if they're alternatives - Consider resolving a NURB to screen resolution, i.e. each pixel ties to an evaluation of the NURB for that point - the end result is that you're moving from a set of continuous functions to a discrete representation produced by evaluating those functions at specific points.
In the most general case, the only way to truly use NURBS and other continuous representations as the only graphical elements would be to return to the old X,Y driven analog monitors, and off the top of my head, I think transparency would be a complete beast at that point. Now, this is pretty much the way ray tracing works minus the rendering to a monitor, but remember that ray tracing is certainly not performance oriented, and at the end of the ray tracer, it still comes down to dealing with individual pixels being rendered in an image plane of some defined size.
It's not the projection of the spline or the NURB control points that's the rub, it's the tesselation/rasterization of the surface, i.e. the movement from a continuous to a discrete space.
What you can do is load up on graphics cards, dedicate a few as compute engines processing the NURBS, splines, and other such functionally defined surfaces into extremely high resolution triangles, and then feed the resultant triangles into the cards actually doing the rendering. Technically, at a high enough resolution you're pretty much indistinguishable from volumetric rendering from the perspective of the cards doing the rendering.
One other thing to consider is that evaluation of complex parametric surfaces can be expensive (or really cheap which is what makes sphere's so lovable) and you certainly don't want to pay the butchers bill for repeatedly evaluating a static NURB on every frame - but then the question comes as to where you will store the discrete data and then you're under memory pressure to identify the flat bits to drop the storage bill
So, a better way of looking at it would be to say that, given a world where the basis definition of a shape comes from continuous surfaces, where and when should the discrete representation of that shape be generated - Ray tracers say not until the very end of the pipeline, most interactive applications say as soon as possible and please don't fiddle with it after that :-)