You are right there.
If you remove Hamura's chakra from the Rinnesharigan then the Rinnegan will appear.
I did not mention it because you were using the Indra - Ashura context. In the Indra - Ashura context, the Rinnegan is the source gene, the Sharingan is a mutation.
This is incorrect since the rinne sharingan doesn't originate from the Byakugan rather the Tree. Hamura's chakra has no bearing on it's existence.
OT: The Sharingan isn't the mutation if anything it's the primal form. The Rinnegan is the complete form of that once all the parts are brought together(rokudo chakra), and the Rinne Sharingan's awakening requires the mezo and the 9 tailed beasts chakra. Hogaromo would've inherited the Sharingan part to pass on the genes, and the fact that Sasuke has a tomoe Rinnegan means he was given rokudo Yin chakra(maintain sharingan yet gain Rinnegan).
You could say that Hogaromo is the human expression of the Jyubi without it's chakra with which he would have had the Rinne sharingan. Kaguya likely kept that chakra restricted to herself and was forced to pass on what she couldn't restrict.
As for the awakening of the Sharingan it's dormant because the gland that excreted the chakra is dormant. It's like a hormone unless there's a trigger it won't manifest itself and do the work. That doesn't affect it's dominance in the slightest.
