Think of it this way they are all part of the same tree
Byakugou= chakra fruit ( only achieve by perfect chakra control, stored over years to blossom a powerful fruit.) remember Byakugou is more than regeneration but it can enhance one abilities jutsu and be programmed to constantly perform jutsu, imagine Sakura programming it to spam substitution , lol kaguya wouldn't even stand a chance . Also Byakugou can connect to others both mentality and physically, sharing power and the mind through a mental wifi of sorts. Tsunade was able to see through Katsuyu, Katsuyu can use tsuande power without asking, I think this is how Mito was able to use kuramas sensory ability without befriending or having Kcm.
RINNEGAN= eye of the shinju
Rsm= body of the shinju
Going by kakshis theory I would want Byakugou, if one could control there chakra perfectly they would therorectically learn any jutsu, and elements can be taught, and Sakura already has yin and yang. Also she has not lacking area now, genjutsu affinity, taijutsu master, ninjutsu genius ( perfect chakra control) and has nigh infinite amount of stamina in conjunction with her chakra control, it's just a matter of writing Sakura correctly.
A chakra enhanced breathe enhanced by the Byakugou will cause a flash freeze and make you say ,"superman who"
