Kaguya spitting a piece of her out can make sense in some way, but it would not make sense anymore as far as the series is concerned simply because that method does not work. This method has been beaten twice, and useless.
Now, according to the story of Kaguya as given by Madara, she was a human who ate the fruit to stop the war. Madara did not mention in any manner that she was evil. On the other hand, Hagoromo's story was a bit different. According to Hagoromo, Kaguya seems to have been a good person in the beginning, but later lost her mind due to accumulating to much power. She became evil and used her Sharingan power via IT to subdue the people since they were scared of her. Hagoromo even said that in her power hungry state, she was called the Rabbit goddess of the moon.
Interestingly, it turned out that Kaguya was almost overtaken by a Rabbit Bijus when she was fighting Naruto and Sasuke. This revealed to us that Hagoromo tale was correct, but he did not know that his mother was controlled by an evil Rabbit biju. Again, he think he was sealing Kaguya, but this time, the Rabbit escape the sealing, and this will give us the back story of both the Rabbit and Kaguya.
