Well .....
I had a brief touch upon this problem before trying out some nvidia code to render quads. But there were 2 problems,
1) the code was crazy complicated handling all kinds of bow tie and other mad polygons
2) it totally blew apart if i duplicated the last vertex making a triangle, which would mean triangles would need a totally separate render path which would seriously suck
Anyway I tried again with the example code in the super bible
This is what a regular triangle looks like with regular interpolation

Pretty bog standard
Anyway this is a triangle rendered with quadratic interpolation with the last vertex being simply repeated

Really quite different. I think i actually prefer the look of the quad version.
This is a quad rendered with regular interpolation (what we are currently doing)

And the same but with quadratic interpolation (what readl3d) is doing

Pretty exciting. I think we can really add these to the shaders with minimal pain really. The code is simple. My best guess based upon non experimentation is, that real3d basically only rendering quads. And that triangles probably shared the same render path. It wouldn't make sense to add a totally separate render path for triangles with their own interpolation code. Most games seem to predominately use quads.