I’m glad that it makes sense 
Embedded is a little tricky for me to describe.
What you mean by adding control points might do what I had in mind.
After all, right now, every time you re-pick the input it gets “Embedded” - the only problem is that there is no easy way to edit it (on objects placed in different places), and also there is no Extract Solids equivalent command which could help to readjust per object inputs.
Highlighting the current problem
Thinking about good examples Subtract & Add Solids came to my mind. You can look on VA Object and (per object) Input geometry the same as on VA Wall and Add/Subtract Solid.
If you move the wall, subtracted/added solids move together with the wall. They can be shown and to some extend edited in the new place. This is very intuitive!
Good example of how it might work for the inputs.
I think my thoughts on Embedded boils down to that - it should be as it is with the walls and solids.
*Only that editing walls and solids could be a bit more direct and comfortable at times, what one user pointed here. But that’s a detail for later.