OK well the so6p had the rennigan, his eldest was a uchiha, and for the record there are so many diff sites that have this story mixed up and everything else....but if uchiha started with the byakugon, and he turned it to sharingan then the byakugon would be no more, he would have created the stop to that. Or EVEYONE would start with the byakugon then go to the sharingan. you can try to translate it all you want. the so6p had the rennigan, his eldest had the sharingan, this is probably do the fact that uchiha had NO where near the amount of chakra as his sage father with a ten tail inside him.
The Byakugan if it is related, which it should be they all are, is the result of a ninja trying to speed up the process of developing the sharingan and pumping chakra to thier eyes, hence EVOLVING the sharingan into the Byakugan. But why hasnt the byakugan evolved yet?