I discovered that _Intersect produces no results for conical-planar surface input not only when the cone is bisected by the plane through the apex and some other control points, but also when the cone’s height to radius ratio is greater than ~3.3097. This occurs in V7.21 and V6, but not in V5. (I did not search whether a different threshold exists in V5.)
V7.21 & V6: V5:
Cone-PlaneIntersectFail.3dm (67.0 KB)