However when I add the child object, the parent object’s pivot point changes to half way between the parent and child. I’m expecting it to remain in the same place as the parent object? Both objects are standard unity cubes.
Is my expectation correct, and if so why is the pivot point moving?
The pivot point is not actually changing. You are seeing the position of the editor gizmo changing because you have this setting in your editor set to “Center” instead of “Pivot”: