Yah, what made Sakura special was that she wasn't special at all. To me she's kind of the girl-next-door type in the Naruto-verse: plain and simple. She stood out, special or not, being MC. But that ambiguity in Sakura regarding everything about her means that there's a lot to experiment with. And one easy, popular way to do so is with fanfics.
And that would've been the surprise of it! Imagine a normal girl, from a civilian family getting to those power levels. That would've been a positive shock value, which wouldn't have been out of nowhere, because the plot laid the foundation to that!
First we have her being called a kunoichi with no special ability. That's point of origin as a character.
But later on she starts training under Tsunade. Yeah, she gets to be a medical ninja, gets her new power-ups.
But then, as the story evolves here comes slight references made by Sakura about Hashirama when Yamato comes into play. How does she know that? Where did it start? Why did Sakura start looking into that to begin with?
Then we have her asking Yamato about the technique. She wants to know more about it. But Yamato says that he cannot teach her that. That's the obstacle that's put in her path as a character that she was supposed to surpass. Why?
Because the mirror to her character stands right in front of her - Yamato. He, too, isn't from a ninja clan, and YET SOMEHOW he was able to withstand Hashirama's techniques and even use them.
Sure the plot then slowly just fades that storyline but like I said, it was always there. Sadly Kishi just gave up on her...
And that's why I took it upon myself to explore those possibilities.
How can a normal, civilian girl with no special powers whatsoever be able to attain such threshold of power?
That's a really fun plotline to explore to be honest.
Honestly I think Sakura would have worked better if in part one she was used as kishi test subject of a sort. He vaguely knew what he wanted Naruto to be therefor because of his stupid balancing the rival Sasuke as well. He didn't know what to do with Sakura.
Instead of just the wave arc there should/would have been several missions like that to help grow the team's bonds before the chunin exam disrupts them. During those kakashi give the group training. Naruto is given task or training to make him become smarter or better control since he already has the body. Sakura would be given more physical training since she already very intelligence. Sasuke since he already has both focused more on the bonding with the others.
Part of Sakura training would be Kakashi trying to figure out what she should do while trying to make sure the team are all doing it together. He tries genjutsu but kishi drops it because it a hassle to do lot of genjutsu fights just to keep her important. Sensory but it turns out Naruto better at it and it help improve Narutos thinking abilities while fighting. Sealing but then it discover to be too complex for her to reliably do with out much experience also she has to spend more of that arc teaching Naruto how to read; who once he does is surprisingly a natural at sealing. Finally, just ending up with Water and Earth to create walls, Naruto gets wind but Kakashi says he not skilled enough to teach Naruto anymore than a few useful jutsu, and Sasuke gets lighting having Kakash decided that Sasuke could inherit his chidori later on.
Then her fight against the sound nin team happens she uses all her ability both what she learned in the story so far and in the academy. However they are so elementary that they are nothing more than an annoyance to the Sound team. sakura realizes that she just been coasting while relying on the other to pick up the slack and resolves to change her self.
By the end of part one she become a medic under Tsunade's tutelage.
In part two during the elemental training she learns she can learn would release which she learns while watching Naruto struggle with the kyuubi during the wind rasengan training filling Sakura with determination to master wood so she could help Naruto.
By the end she would have surpassed her master. The evasion, healing and power to defeat her foes from Tsunade in a single hit. But also genjutsu to debilitate/distract her foes, earth, water and wood to protect her allies, and some knowledge of sealing and sensory abilities.
As for Naruto fan fiction in general. I find less preaching at church and less sophistry in a college dorm than I do in a general Naruto fanfic.
Yeah, the exposition regarding her character wasn't the best. But I thoroughly believe he had something in mind for her because like I said on the other reply, the basis of that foundation was there. He seemed to be having a pretty clear road up to a point when he just let the popularity polls take over while being flooded with hate regarding her character.
If he would've just stood true to his own plan, I think that maybe he would've seen a different reaction towards Sakura, but he failed to do so in the end.
She had the potential to truly be the deadlock between Naruto and Sasuke.
I also think there was a plot for her genjutsu abilities as well, but more like in terms of dispelling one rather than creating one. I think he meant for her to even go as far as to dispel Uchiha level genjutsu and that is tied in her Senju lineage connection.
Because think about it - Senjus were superior to Uchihas in every way - that included their genjutsu abilities as well. So then it begged the question - how exactly?
And I think that Sakura's connection to their storyline would've answered the question if not for him dropping her character alltogether.
So... I have feelings about Sakura. lol-obviously! 
I think it's too easy to see Sakura as just the 'normal one.' Even though she's definitely portrayed that way in the manga, over and over again. It's too simple of a description for her. I think she's got so much more going on, but it gets swept aside from her lack of backstory or evolution of character.
In fact, instead of finding her more normal, I just keep finding more and more ways that she and Naruto are alike!! Both are powerful but come from unknown backgrounds. Both are 'orphans' in their world: neither has family support/presence in their shinobi career. Both had minimal training to unlock their abilities, and both from the two least-teachery teachers of the Sennins (Jiraiya and Tsunade). They are both misfits in a way (Naruto is the class slacker, Sakura is bullied), till they find each other. Then of course, both grow together, have the same motivations, admire each other and never give up.
It is shocking how perfectly suited they are to each other, for him to end up with Hinata who he has NOTHING in common with.
Back on topic, since Sakura was billed as 'the normal one' of the group, it would make sense for her to be revealed at the end of having some ancient power. Perhaps even latent, which is why she a had non-ninja family. She doesn't have to be special like that, but it totally feels like it's being set up in the manga for that outcome. The normal girl turns out to have some ancient power in the end that saves the hero. (But of course, her growth in the story stops after the Pain arc. So we'll never know.)
I actually think Sakura has an untapped power that even she didn't know about (like Naruto growing up). She is so much more powerful than everyone else, even Tsunade. In that way she's never been a 'normal' girl even though she grew up in a normal home. She's always done twice as much as her team and all her other classmates, and then still outpaces Tsunade's abilities in the end. None of the other rookies does what she does.
Imagine if Lee, the closest comparison to her skills and journey, were to become a go through med-nin training at the same time as his shinobi training, come out and become a doctor and a top-notch ninja, then surpass Guy's abilities...and then surpass the Kage's sage level!! That's what Sakura does, and yet people still think she can't carry her own weight!
So like I said, I think the normal girl set up would have been that much sweeter if she was revealed to have a more complex power/background in the end. But if that was the plan, we'll never know.
There is a whole medic storyline built into the manga. Chiyo was a medic. Tsunade was a medic. Orochimaru was a medic. Who taught them? There are clearly healer types and warrior types, using the same medic abilities.
As for fanfic.... muwahahahaha! I have thoughts on this too! 
If you read my fic, Voice in the Wind, Sakura's story development is a major point....
Sakura has to uncover the origins of her own power. And that even though she thinks of herself as 'the normal one' on the team, she comes to realize that she's not. She's an 'odd one' just like the rest of her over-powered team. She discovers she has a hidden power that some people know about and can even see in her, while most people don't know. Which is exactly like Naruto's story. So she has to come to understand her unique chakra capabilites, with people who want to help her, or hurt her, or use her. Again, just like Naruto.
The next chapter breaks all this open, so I'm not exactly spoiling the plot. Just giving a little preview!
Anyway, love this thread! I could talk/read about this for days!!
Exactly Tricks! It's like... why make her look as the normal one to begin with? Why put her into that contrast if you're gonna let her just be that, while also tying certain elements of her subplot to one of the strongest ninja clan out there. Not one actually, but two - because there's always this connection to both Uzumaki and Senjus.
Not to mention the clear alluding at the forehead symbols - both Mito AND Hashirama have those forehead symbols. It was clear as daylight that she was supposed to be tied-up to them.
And yes, Naruto and Sakura have so much in common it's amazing to me that people didn't see it. It was always there. Sure, he had some minor things in common with Hinata too - like being the outcasts of their respective environment, but other than that, that was it! Sakura and Naruto have more than that.
They are mirrors to each other - like Heaven and Earth! No wonder Kishimoto gave them this symbolism!
And it's one I am very much building the story upon as well. Heaven and Earth are nothing more than a mirror to each other - both use energy at their core - one is body, one is spiritual.
It's like us with our human shell on earth and our higher spiritual self. I think Kishi also wanted to go this route with her via Inner Sakura tbh. I think she was meant to be MORE than just a fanservice comedic aspect. And that had a laid foundation back in her battle with Ino, when Ino tells Sakura she has two minds.
What does that mean two minds?
The signs were always there for her to unlock like you said, this ancient power. And that can happen with her being from this normal civilian family.
That's what I'm basing Kaika on.
The normality aspect with her was always in juxtaposition with characters such as Naruto, Sasuke, Gaara. Kishi even says that she has no dark secrets or stuff like that. There's no tragedy like that surrounding her clan.
But no dark secrets or tragedy doesn't equal coming from a clan with no special ability. That's the thing. And that's the card I'm also playing with Kaika, like you're playing with Voice in the Wind.
Because think about it in OG storyline - who else had the same knack for chakra and easily climbed stuff? Right, Hashirama Senju.
Despite not being from such a well-renown clan, Sakura displays the same understanding and ability for chakra. She just doesn't have the stamina.
But the stamina can be trained. Such knack for it from the get go, also means there's something there. Her understanding of chakra and effectiveness in using it is something that surpasses most cast.
It's something I actually already started tapping in the second chapter of Kaika's.
For who's interested by the way, the new one got posted in its dedicated thread.
