I don't think you know Hagoromo nor feudal japan that well.
All black Zetsu was doing was goading Indra, obviously Indra would mever hold a camdle to his father though

. This isn't the first time someone in Naruto was blindly manipulated. Black Zetsu's manipulation of Indra and his descendents, Madara manipulating Obito,Danzo manipulating the foundation and Sai, the entire "ninja creed" under the second hokage regime of what it meant to be a ninja, heck even the third Kazekage was blindly manipulated by Orochimaru. All it takes is a little push, Indra already felt that he was special all one had to do was give him enough incentive and inflate his ego. Sure as heck happened to Madara and Nagato (before Naruto TNJ).
Hagoromo already elaborated that Ninshu wasn't supposed to be weaponized in canon. That's ninjutsu, idk what you expected from a humble munk that is Hagoromo. It sounds like you want someone that is constantly showcasing godly power and putting nations in an awestruck stance everynow and then...That has never been his character. That's not even in the character of a monk even in canon Hagoromo was quite modest even when Filler started I knew he wasn't going to ne showcasing a lot of godly power given from the character canon gives us of him and I was right, and I'm not even a Hagoromo fan.
And afraid or indifferent to confront Indra? He literalky talked to Indra about it. He said if Indra didn't someone would and praised him for his intuition that Indra's innovations could be weaponized. Hagoromo always believed in the natural order of things. Even in canon when Sasuke captured the bijuu and Kakashi questioned him. Hagoromo simply stated it would be selfish for him to do much of anything and intervene with how things "should go". That's typically what people have issues with when ot comes to monks or people of high power and status. They don't intervene unless it A) harms their existence B) ansoliteky necessary or C) a combination of both.
To answer your Indra question, nobody tells their parent everything. To Indra black zetsu is a makeshift subpar ally. Even if he did tell his father it's not like he or his father could answer who he was. It could've been some random. Indra didn't even tell Asura and if he can't tell whom he loves most he isn't telling his father. It is questionable but black zetsu manipulated Indra in a way that he goads him and praises him for his talents. As far as Indra is concerned he's just sone random that happens to be right about some things such as gaining a sharingan. Black zetsu even told him not to worry about whom he was.
In truth just because it's filler or anime doesn't mean chatacters aren't still human and don't make hunan errors. Hagoromo said he was going to explain the story of Indra and Asura not gloat about how strong he was.