The problem here is you are going off the assumption that Hagoromo shares his powers with Hamura in order for him to fight along side him, when you have no actual proof of this. As you stated you are using an Anime filler to form a hypothesis that lends to the notion that Hamura could not fight along his brother without his aid.
This was never stated not proven I’m the manga, anime, or The Last. Hamura May have been somewhat below Hagoromo’s level but that doesn’t mean he was incapable of fighting by his side. We’ve seen what Otsutsuki can do without Sage Mode or a Rinnegan (reference Kinshiki) Hamura was Kaguya son. Directly from her womb just like Hagoromo.
He is still god tier if that’s what you’re asking. He just isn’t at Hagoromo’s level though the power gap is small. Things got rushed and haphazardly put together at the end of the series so things were not developed on Hamura’s end as they should of been, hense why he was the subject of matter in The Last; to give more background on his character.
Again, you basing a huge portion of your hypothesis on “filler” info which quite often contradicts, and sometimes, downright ignores manga material.