The "distortions" of the two-point system can be readily observed in this display. The top edge of the image rectangle is the horizon line, and the two recessional points are in the upper left and right corners.
The gray slabs distort as their shapes extend toward the bottom of the rectangle. But the green cubic form, sitting in the center near the top of the field, appears without marked distortion.

To summarize, the logic of point-perspective systems is not the logic of our three dimensional perceptions of the external world. Parts of it seem to fit well enough, but the system as a whole will always contain visual distortions.
Secondly, other types of systems will produce other perspective grids with interesting, if useless, space projections. These help to stretch the imagination and deepen our wonder.