Stupid question: Why not use the hardware (fixed function) rasterizer inside the GPU? I guess that one is only optimized for triangles.

The longer answer is that using straight-edged geometry to represent curves is a resolution-dependent operation, e.g. a full screen circle may need to be flattened to an 80-sided polygon.

Rasterizer can solve quadratic curves in the fragment shaders, which massively reduces the geometry needed for a scene.

Also, the native rasterizer only supports MSAA, which is inferior to reference analytic area AA.

Good question and answer ;-)