Well,the way I see it is....kishi has always wanted to give the byakugan more importance. If you remeber in part one.kishi set up the lore as the hyuga being decendants of the sage due to their dojutsu. It was also praised for being better than the sharringan in visual prowess. That being said I think kishi always meant to do more with byakugan,but for one reason or another kept having to put it on the backburner. Giving kaguya the byakugan is his way of connecting the hyuga to the bloodline and give the byakugan the shine time he always wished he could.
Personally I belive its a tad deeper than "gods have white eyes"
yeah I know where you're coming from but it's just the stereotypical thing all godlike animated characters have it. Like white eyes kaguya is no exception.
however back then that's a thought but back then kishi admitted that he wasn't even sure if shikaku and kurama were related he can't plan ahead for everything authors will make changes and revisions.
it's also a rumor the sharnningan came from the byakugan which in itself was proven wrong. Neji boosted how superior the byakugan was however during the ninja war the senju and uchiha are considered the strongest no hyuga was included.
the byakugan is good stemming from kaguya to hamura to the rest of the descendents. What would be added to the byakugan the sharinnegan basically already gave kaguya all the abilities she needs the byalugan adds its input as well. Seeing from kaguya that's how the byakugan is no further evolution. It's just placed there to give its place as a great dojutsu, godly status, etc.
Well imo kaguya looks better with the byakugan than the other eyes if she had the other eyes she'd look weird. Each dojutsu is meant to be different the byalugan has it's unique qualities just like the other dojutsu's