Poly Carve SOP can also carve closed polygons where it will still use the points but instead of creating multiple curves, it will keep a single polygon.
This method will carve geometry like a torus as you expect.
Because of this, the higher resolution the surface is, the more detailed carving you can achieve.
Here I used 2 separate nodes for ease of use, but the same result can be achieved using a single Poly Carve node if you have the appropriate primitive attributes on each branch.