The ootsutsuki's

[InfiniteMugen]

Unless you didnt pay attention, allow me to point it out to you:

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Kaguya and the lot have the power to turn lifeforce into power.

Here we see Kinshiki giving up the remainder of his life to become a chakra fruit to which Momoshiki devours.

We also hear him say that his predecessor had done the same for him.

We also see that Kaguya eating the fruit (which is actually the tree).

I take it as more the "I eat weaklings like you for breakfast" kind of thing.

They eat people so they can grow stronger.

Hmm.... Yea I wasn't paying attention at that part... At all apparently lol so basically they just wanted her to take her power?

 

[Scryed]

The Ootsutsuki clan apparently went from world to world looking for power.

The power Kaguya acquired just so happened to be the God Fruit.