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I believe that in the above scans it could be inferred that chakra was always dwelling within humans, and Hagoromo simply spread Ninshuu around the world (basically teaching people how to use the chakra to bond with each other), instead of him actually giving chakra to every single person and animal in the world.
There also the fact that it's been stated that the Shinju grows from the blood of humans.
How does something that is basically a manifestation of chakra grow from something that contains absolutely no chakra? It doesn't, like plants grow via water and they contain water.
Kaguya was simply power hungry and decided to take the chakra from humans while under the delusion that she owns ALL chakra.
Then there is the fact that in olden times Kaguya used IT to enslave humans, and how is it possible to use genjutsu on something that has no chakra? You can't, it's impossible.