For generations since Ashura and Indra, the successors were always uchiha and senju. Those two powers combined = hagoromo.
It's been widely speculated and it makes sense that Hamura was represented as hyuga and uzumaki. Assuming he didn't have children, the two clans should have been out of the equation, and even if he did have children, they would have their own separate transmigration (assuming there was a struggle)
Essentially we may have a cross-transmigration where Hagoromo and Hamura's successors have mixed.