Her character would be completely different if she was a Hyuuga so we don't know. If she just randomly got the Byakugan she would be much more useful. But she would not have mastered her god like chakra control and healing prowess and wouldn't have Katsuyu. All of those are very useful. Plus Sakura is a smart girl, she is smarter than Naruto and maybe even smarter than Sasuke. Unfortunately the team didn't go on enough dangerous missions to make use of her healing and Katsuyu so being a Hyuuga would be better. They definitely needed someone with a Byakugan in the forest of death as that would have proved to be very useful
This is true which is why Kishi didn't go that route. And it would have been great if he had flushed out her medical training with what her original type is (genjutsu)
Both Sasuke and Naruto got trained and developed everything Orochimaru and Jiraiyah had in addition to their own unique abilities. Kishi got lazy with Sakura and just made her an exact copy of Tsunade...lol even Jiraiyah made that comment when he first watched Naruto and Sakura take the 2nd bell test XD
I wouldn't have minded if Sakura became a genjutsu specialist capable of rivaling even Uchiha Genjutsu. That way she could still represent normality while not being completely negated by development.
Look people keep going against Kishi’s plan for Sakura,Some keep saying She was going to be Sage others keep saying She from a Clan and on an on. Kishi stated Sakura was meant to be an ordinary girl only so deal with it. All Sakura had was big dreams of Marring Sasuke and She did,that was Her ultimate goal.