Good suggestion. Two thoughts:
First, this can be done as a workaround by encapsulating the animation in a group that is sized to the stage. Visibility of overflow can be turned on and off via the inspector.
Second, another feature request has been that of preventing the view to be centered on a selected object / forced focus on center stage, without which the stage can be thrown around the screen. Until this is implemented, the visibility feature could lead to some confusion.