I think that a dedicated tool is needed, since Catmull-Clark subdivision works in a different way than NURBS. For NURBS surfaces it’s just enough for the symmetry tool to take into consideration the position of the points from one side of the mirror plane and apply the opposite coordinates to the rest control points, as seen in the video with VSR for Rhino 5 above.
Ah, right. Well, I would defer back to this post then… screw the technical reason, the UX should be the same, so the tool should be the same! 
Since there are two different types of geometry, obviously the tool should be able to guess which one is under editing, in order for two different codes to be combined into a single UI menu. 
Tools such like “Trim”, “Split” and “Rebuild” prove that they can work with variety of geometry, such like: points, curves and surfaces. “Trim” and “Split” both work with points and polysurfaces, as well.