The early Evans & Sutherland ESIG line of image-generators (IGs) employed the technique in hardware 'on the fly', to generate images one raster-line at a time without a framebuffer, saving the need for then costly memory.
The Nintendo DS is the latest hardware to render 3D scenes in this manner, with the option of caching the rasterized images into VRAM.
It proved better than Z-buffer/painter's type algorithms at handling scenes of high depth complexity with costly pixel operations (i.e. perspective-correct texture mapping without hardware assist).
Sony experimented with software scanline renderers on a second Cell processor during the development of the PlayStation 3, before settling on a conventional CPU/GPU arrangement.
In modern Z-buffer systems, similar benefits can be gained through rough front-to-back sorting (approaching the 'reverse painters algorithm'), early Z-reject (in conjunction with hierarchical Z), and less common deferred rendering techniques possible on programmable GPUs.
The Z-buffer allows larger volumes of primitives to be traversed linearly, in parallel, in a manner friendly to modern hardware.
Transformed coordinates, attribute gradients, etc., need never leave the graphics chip; only the visible pixels and depth values are stored.