Do I really need to use a planar rectangle and boolean split to get what I want?
Why can’t solid manipulations be more intuitive? When edges and vertices get overlapped, Rhino should automatically collapse them. Is there a command to do this?
Two ways to do it -
Extrude surface DeleteInput=No and then BooleanDifference from the main object, or,
Extrude surface DeleteInput=Yes - which does the above in one step.
Then MergeAllCoplanarFaces.