MDG, the same rason it is not Muktza on Succos, although it is a Derabanan, it would not be Muktza on Shmini Atzeress, had it been a Mitzva. The main reason is as was posted above: it is a Bizayon of Yom Tov.
Akuperma, there is absolutely no Safek of which day is Yom Tov. If it would be a Safek, we would have big problems with rollover Sfekos, and Yom Kippur. It is a Takana that we should have a system in place in case we lose the calendar.