Your theory that he mated with someone is just as good as my theory that he created them.
Both are baseless, and have equal chance of being true.
But my theory holds more weight since indra and asura get reincarnated like the bijuu.
Sorry that is not true at all.
If we see an egg in a grocery store and I tell you that I think this egg came from a rooster, and you tell me the egg came from a hen, since both of us didn't actually see where that egg came from, is my theory of the egg coming from a rooster just as good as your "theory" that it came from a hen?
Of course not, because by default hen lay eggs and not roosters.
The same concept applies with our discussion, Indra and Ashura were introduced as Hagoromo's sons, by default we assume that they have a mother of whom Hagoromo mated with to have them. Just like we assume that Kakashi was born from Sakumo's wife.
I can say that I think Sakumo infused white chakra in his white fangs and pierced the ground and Kakashi emerged from the ground and that is how he was born, I can not say however that my theory has an equal chance of being true as the "theory" that Sakumo mated with someone to have Kakashi, you catch my drift?