Arguably the biggest thing Kishimoto could have done for Sakura's character was decide exactly what he wanted for her.
He wanted to add a girl to the mix to balance out two boys, done.
He wanted to create conflict in the team dynamic, done.
He wanted to create romantic tension, done.
But what else is there? He has a female teammate balancing out two hot headed boys in a love triangle. What else does he want to do with her character? He started showing that Sakura started from being a snooty fan-girl and child who has no real experience with ninjas due to her civilian background is slowly learning to grow up and mature as both a ninja and a person.
She is being exposed to the reality of what a ninja will face, will encounter, and what is expected of them. Being a ninja is a dangerous occupation and it's not a game or an occupation where you can clock in and out at the end of a day. She is slowly discovering this in their adventures, such as in the Wave arc and then in the Chuunin exams where they have to sign a waiver to even compete! There is where her self-discovery of her lack of skill comes to light and she makes a goal of improving herself so that she won't hold her team back anymore.
Unfortunately, we get the drive to better herself, but we don't get the execution of her actually improving. Like many have mentioned previously, Part I would have been the perfect place for her to strive for a goal of some sort. If having her eyes opened to being an amazing medic was her goal, it would have made perfect sense for her to approach Tsunade and especially if she were to witness Tsunade in action and be inspired. Otherwise it just looked like she went to find the strongest ninja she knew of to plead to become her teacher to help her improve, but did said teacher's skills and abilities align with her goals? Hm...
It was also in Part I where Sakura had declared that she loved Sasuke enough to the point where she was willing to leave the village, her home of thirteen years, to be with him. Granted you could write that off as being blinded by love because love makes you do stupid things, but what was her reason for loving Sasuke to that degree? Sakura started off being shown as liking Sasuke because he's good looking, he's smart, and he's a skilled ninja. It's a crush before they are formed as Team 7, but what about after they've been a team for a year? What about Sasuke transformed those feelings from crush to love? She started understanding Sasuke's reasons and feelings for why he must avenge his family, but her character wasn't written or shown well doing that and that her feelings started developing into something deeper, whether it was friendship or love.
Then there's the issue with how Sakura treated Naruto. This is probably something harder to overcome since first impressions are everything and she wasn't necessarily given the best first impression. For one, she is shown fawning over Sasuke and then immediately being annoyed by Naruto's presence the next. Even though she started learning to treat Naruto better because she started to understand how it feels to be treated as annoying and then later developing a friendship, her growth was slow in Part I. We can see that she still treated Sasuke better than Naruto even though they grew closer. It's not unrealistic, but since Naruto is the underdog, fans would want for Naruto to be treated better and this change in treatment was probably too slow to curb the Sakura hate.
As many have mentioned before, Sakura is always being overshadowed by Sasuke and Naruto. There is no information regarding her background, her dreams (not counting Sasuke), goals and ambitions, her skill set, and what she will grow to be. In Part I she didn't really participate in any fights outside of the Chuunin exams and the Wave arc. Meanwhile Sasuke is being taught more techniques with private training, Naruto is left alone but somehow bumps into Jiraiya and is taught how to better control his chakra, while Sakura... does what? There were many instances where Sakura could have some relevance to the story or even small moments showing support for Naruto (since Sasuke went into isolation for training) but Kishimoto didn't even allow her that. I thought they were friends at this point and isn't that what friends and teammates would do?
Sakura's character wasn't that bad to begin with. It's always better to start with a slightly annoying and flawed character and watch them grow to be a better person. In Part I there were many missed opportunities and threads that he could have used to prepare and further Sakura's character growth for Part II. Sakura's character was still growing and evolving during Part I but it was too slow and underdeveloped compared to other characters and story lines to garner fan interest.
Then came Part II and we see a new and improved Sakura. She's a skilled medic, powerful fighter, and a great friend to Naruto. She always puts his well being first and after finding out the burden of housing the Kyuubi she even despairs about how she is unable to help relieve Naruto's suffering. But then soon after the story became more plot driven and less character driven. In Part I the writing was heavily character driven for a lot of the characters and not just the main characters whereas in Part II it was more focused on plot. As a result, we see power up after power up, focus of the story being shifted, and plot turns after plot turns. Many emotional beats were either lacking (compared to Part I) or fell flat and the focus was rooted solely in the Uchiha clan. Let's not forget lesser and lesser screen time and character regressions as the manga ended either.
All together, Kishimoto didn't have a bad character to start off with. He just needed to develop Sakura more in Part I to strike a chord with readers because Part I was when he was best with characterizations and would have been a good set up leading into Part II. Despite his portrayal of Sakura's growth into being a very caring person and great friend in Part II, all her growth and maturity went out the window when Sasuke was involved because Kishimoto decided not to make it clear what lingering feelings Sakura has for him. Is it longing for a lost love? Longing for a lost teammate or friend? Is it none of the above and she just wants him back around friends and not around a creepy snake? Which is it? And what happens after Sasuke returns? What does she expect? He introduced conflict when Sasuke was officially declared a threat but her reaction feels confusing to the readers when we don't even know what she wants to do or what she feels.
And why did he decide that he couldn't include more of her skills? What exactly did she learn other than what we expected? Kishimoto could have showed us what her end goal was too. Was it to be a medic? The best medic in Konoha? The world? Or was it because that just happened because she trained under Tsunade? He basically had Sakura's character started at A--> B --X--> C but didn't end successfully at point C (end) because she's still stuck in point B throughout all of Part II.
If Kishimoto really wanted to improve Sakura's popularity he should have at the start of Part II started developing her the best he could to make up for lost time by providing an arc for what inspired her to become a ninja, why she wanted to be a medic, show audience how she grew and how she got to that point so that we're rooting for her journey too. And since he established the strong connection between Naruto and Sakura already, he should have just kept it going strong instead of letting it fade under all the other events going on.
Oh and Kishimoto should have asked for advice from people who have experience in writing strong female characters or doing some sort of research to get an idea. Or he could maybe host a fan meeting and throw out questions like what fans want to see next in the manga? How do they want X Y Z characters to evolve in the manga, etc to get an understanding of fans likes and dislikes to determine how he could overcome those barriers.