Currently if you copy a body from design "A", and try to paste it into design "B", you get one of two behaviors depending on how design "B" is set-up.
If "B" is a non-parametric design, you see the copied body appear as expected.
If, however, "B" is a parametric model (capturing design history), then nothing happens. The reason is because Fusion is expecting a foreign body with no history definition to be pasted into a Base Feature. An application just not doing anything or not providing any user feedback is poor UX design.
Instead, it would be nice if Fusion recognized this condition and just automatically created a Base Feature, or at least prompted the user if they would like one created.