Pardon me I didn't read everything, I read just from the latest comment of Elveonora. Now considering the anime, wouldn't it be possible that Hagoromo actually didn't know about Ten-Tails as Kaguya in the anime? as he has fought the entity separately so it would make sense he didn't elaborate that in flashback, he might have thought that ten-tails was being controlled by Kaguya so sealing Kaguya means controlling Ten-Tails. I'm sorry if I'm confusing you guys. I know it's a contradiction to the manga but I'm somewhat iffy about it.
So just to clear this up, in the manga the panel where they are shown facing the ten-tails (which is also shown in the anime) they mentioned about sealing ten-tails, I think this would fit if Hagoromo actually didn't consider Kaguya as a threat at all just the Ten-Tails. Just a theory that he might have considered Ten-Tails which has surfaced (in Naruto's time) to be a threat, so he gave the power to eliminate the threat, this would be in line with the anime. My thoughts are - Hagoromo might have thought that the Ten-Tails is a power vessel that has a mind of its own. The person like Kaguya or Madara gave the Ten-Tails the power (Ten tailed beasts chakra) to activate itself. Making it a major threat as compared to Madara or Kaguya. The switch lies in Kaguya or Madara, but he told Naruto to seal Ten-Tails which might also work or so Hagoromo thought in this case, just a theory.