You can reduce the percieved artifacts of non-perspcetive correct interpolation by subdividing the texture-mapped triangles into smaller triangles (why does this work?). But, fundamentally the screen-space interpolation of projected parameters is inherently flawed. In this example the front face of the right cube is subdivided into 8 triangles
and screen-space interpolation is used. While the artifacts of this approximation
are less obvious, they can still be seen as you move around the cubes.