Hagoromo is the essence of a fallen or misguided sage within Buddhism.
He sought power that was not his own in the Juubi. He interfered with the natural order by passing that power to humans. He expected that he would be able to influence and/or control how people used that power through the choosing of inheritance by his sons.
He time traveled because he could not stand to part from the affairs of the world and leave it to its own devices.
He saw himself as the world's messiah and as the one responsible for whether or not the world could achieve an ideal of his arbitrary choosing.
Hence the Gedo Mazo - Literally translated "Outside Way Demon Sculpture" - or the statue of demonic misguidance.
Naruto's character up until after he spoke with the Sage and inherited his power was to seek understanding in his opponents and in the world around him.
Despite Kaguya being a -seriously- bizarre case and obviously troubled, Naruto attempted none of his usual behavior. He made absolutely no attempts at peace, and just decided it was good to go ahead and seal this person away indefinitely (a fate any rational being would attempt to avoid at virtually any cost). He made no appeals to her humanity, he was, for all intents and purposes, completely out of character.
While I suspect that was partially the effect of rushed writing - Naruto also does other things, such as saving Gai who used a sacrificial technique.
A friend of mine who is watching the subbed anime only just saw Gai's sacrificial scene and said "You know what would piss me off, is if he would be saved, somehow... it would completely negate everything he just did."
Even Gai accepted the consequence of his actions being the end of his life. Naruto's saving of his life through the use of inhuman powers is exceptionally questionable. Just because you 'can' doesn't necessarily mean you 'should.'
Consider how the real Taoist sage of the series handles it:
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It's actually another interesting extension of the theory I stated.
Where did that sealed part of Kaguya go? Her compassion?
None other than Hinata. Still a goddess of uncontested capability, but stripped of her power.
It was Hinata who inspired Naruto to overcome his challenge during the Chuunin exams. It was Hinata's sacrifice that inspired him to end the 'cycle of hatred.' It was Hinata who salvaged him from despair during the war.
Hinata brought the world together in a way her all-powerful former self could not. Like a true Sage, her actions are almost indistinguishable from those of nature, itself. Of course, Hinata is probably not consciously aware of her relation to Kaguya as being the reincarnation of her heart.
If the movies continue long enough, it's possible that such a plot as the reunification of Kaguya and Hinata could occur. Technically, the issue of Kaguya and the Fruit have not been completely resolved. Kaguya is sealed, but the seal can be undone, again - and that'd be a problem since what Hagoromo did is contingent upon him being able to pass powers along... which it is implied he was only prepared to do once.
The fact that Sasuke was on the trail of information related to Kaguya in the Gaiden series is a hint that the issue is not fully resolved, either.
Of course, what Kisimoto made canon is considerably different from the story I've postulated, so if he were to go with certain ideas I consider to be "the original plot," then he would have to insert them with retroactive continuity.