And as a quick addition (I put this in a reblog because the original post is meant as a general issue while this one is more specific), Sakura's character is often criticized and labeled as "badly written" because she never overcame her mean-spirited attitude nor her crush on Sasuke. Yet, this personality trait of hers never caused her any major problems within the narrative as she still had a group that supported her despite her egoistic attitude and her constant seeking for validation (diminishing other people's value in the process, like she did with Tsunade); furthermore, they reacted to this search of hers by bending to her will and validating her --so she obtained what she sought, why would she change her attitude if she gets what she wants? Even her insecurities and need for recognition are in line with her narrative stance, she's the teammate of not one, but two children of prophecy, of Indra and Ashura's reincarnations, people who surpass every shinobi ever; she's quite canonically the third wheel in the team as she's nowhere near their level of strength. How can she not feel minuscule in the face of such a display of power? no wonder she seeks constant validation over and over again.
Also, many of her stans (usually anti-Sasuke rabid fans as well), tend to look at her crush as something that does not possess logical sustenance, when they leave aside that Sasuke as a target has little to do with him in itself but with the status that he could provide her within the military and social pyramid of her village (Sasuke is Ino's upgraded idea, get it? her arc is exactly the same one as when she was a child). Not only that, but Sakura is told tirelessly that Sasuke is not capable of making reasonable decisions since he is blinded by "darkness" which means that his constant rejections are not a consequence of a real lack of interest in her on his part, but his refusal to "be happy". If her entire environment believes that Sasuke's decisions are based on a "biological curse" that controls his feelings and decisions, therefore his rejection and violence towards Konoha and his former team are not taken into account, why should she make a decision contrary to that of her group? Why would she decide to "let Sasuke go" if not a single other member of team seven is even willing to consider it? Her pursuit of Sasuke is no different from the actions and attitudes of the rest of her social environment who also refused to "get over" their fantasies about him.
Regarding her characterization, Sakura is an ambitious woman who grew up in a universe that values strength above anything else (they give the title of Hokage to the "strongest" one) and saw that she was surrounded by monsters with a power that she could never dream matching, such thing gave her a level of self-esteem so abysmal she sought validation through the connections she formed through her life: Ino, Sasuke, Tsunade... and constantly wanted to prove to everyone around her that she surpassed every single person that gave her a helping hand because all of her bonds are formed over the premise of "competition" as that's how ambitious she is (that's the system dogma, as well, as allowing and encouraging rivalries is a primary example of this mindset). Sasuke, as I've stated, represents the culmination of her goal: Status and power, through him, she has it all, so in her eyes, why not pursue him?
There's also a nexus regarding beauty and status that Sakura makes, as she considers Ino to be beautiful during their childhood (I guess such an idea hasn't changed later on as she seeks to insult Ino's looks to diminish her relevance and power level during their match and later on when she wants Sai to insult Ino in the same manner he insulted her) and comments on how beautiful Tsunade is (the only one able to help Sasuke when he was put in a coma), so it isn't strange how Sakura cares so much about how desirable other characters consider her, as the two women that she saw as role models were "beautiful" for her -Sasuke is also incredibly beautiful, so beauty=elevated status is a parallel she draws.
Her fandom also draws a parallel between beauty and status, on a much bigger scale than Sakura canonically does, as they make her out to be this beautiful woman everyone desires and starts wars for (Kakashi, Itachi, Madara *enter any Uchiha you can think of here*); this is quite common in real life as well, as capitalism and patriarchy also encourage women to look as beautiful as possible to "reward them" when they fit the standards they seek: I've said so before, but many of her stans hide behind the term "feminists" when their real interest is to prove their self-insert is "desirable," as they make the level of importance of certain characters within Narutoverse be measured based on how beautiful/powerful their husbands/partners are.
Many stans take the beauty of the male they imagined her with as "proof" of how attractive Sakura is because desirability = beauty = power. Even their need to show how "powerful" or "strong" she is (often by providing examples of how "superior" their fav is to other female characters) is more about them being recognized, admired, and desired by the male characters. There's a reason why they make them praise her all the time in their stories or why when a man canonically recognizes Sakura for whatever reason he gets immediately rewarded with a shipping fic (Kakashi!); hell, even why this lack of reward to their praisings makes the Naruto dudebros hate her for her lack of reciprocation. This fits the patriarchal and capitalistic narrative all too well, as for them beauty provides a superior position from others, being that people within a privileged economic position has more resources to "fit the beauty standards" they set themselves, cementing the notion that "the cute ones belong with the cute ones (economic/political status ↑), while the ugly ones belong with the ugly ones." (economic/political status ↓).
I understand why Sakura would think this, as this is the standard set before her by the society she grew up in -but her fandom behaves with the exact same mindset while critiquing patriarchism (although these "critiques" are superficial at most) and chewing Kishimoto up for not giving Sakura the reward she deserved and instead throwing her to the cold hands of misogyny, yet they regurgitate a version of hers that abides just by the same standards they so eagerly claim to condemn.