I do not know the mathematics behind sub-d but my intuition says this should be possible and I see a lot of applications if this functionality exists.
Mock-ups and a better detailed description of what you envision would help. At the moment I fail to see what you mean.
Thanks for the request, the ability to collapse a SubD face to a vertex is filed as an internal feature request currently RH-49668. As you noted, you can already delete a vertex to make a face via sub-object selection. There is a mesh command called CollapseMeshFace that does the opposite on meshes allowing a face to be removed/collapsed. This is not hooked up for SubD yet. You can use ExtractControlPolygon to try it on the control mesh of a SubD and then ToSubD to convert it back to see if it is what you’re looking for.
I did find an issue though when collapsing Ngons like in your example. I filed this as https://mcneel.myjetbrains.com/youtrack/issue/RH-56609