i was just wondering what's the use of the CP, Srf CP, Crv CP components, when you have the pull point command that practically accepts any geometry as input (including points, curves and surfaces)
you might want to know more about the curve AT that closest point. What if you wanted to know the curvature at the curve at that location? You need the curve parameter to get that far. Only CurveCP will get you there.
Usually (at least for me) you want the curve parameter or the uv coordinate that corresponds to the closest point, and not the actual closest point. Those outputs are not there in pull point.