Have a duplicate object with no offset
I never want the duplicate to have both a vertical and a horizontal offset. If I want to make a small change to the object for an animation, or to rotate it with respect to the original, I want them aligned. Otherwise, I nearly always want it horizontally or vertically aligned with the original. I realize this would violate the convention that every action have a visible result, so the offset is a reasonable default for the beginner. However, I should have a setting to eliminate the offset (as in Inkscape).