While the idea of Vegeta not being able to go Super Saiyan seems preposterous especially given the current landscape of Dragon Ball continuity in which Vegeta has literally unlocked the power of a god, the truth is–based on the originally established lore–Vegeta simply doesn’t have what it takes to unlock that specific ability and therefore should have never been able to in the first place.
Vegeta made his first appearance in Dragon Ball chapter 204 by Akira Toriyama, and upon his debut, Vegeta wasn’t the hardened-but-loveable hero fans know him as today, but was instead a cold-hearted villain. Vegeta first encountered the Z Fighters he would later call his family when he was literally killing them after invading Earth with the intention of killing every living thing on the planet. In fact, even Vegeta’s redemption arc isn’t without the murder of a few innocent bystanders. When Vegeta turned against Frieza and ended up partnering with the Z Fighters on Planet Namek, he still wasn’t a good guy and Vegeta even killed an entire village of Namekians just to get his hands on a single Dragon Ball. Not only that, but even before Vegeta was introduced he committed countless atrocities on hundreds of planets he conquered in the name of Lord Frieza. Vegeta’s soul is stained in a way that can never be cleansed as the spirits of his countless victims will forever swirl in torment over the heartless acts of murderous violence Vegeta committed against them and their loved ones.
In Dragon Ball chapter 319 by Akira Toriyama, Frieza and Goku are in the middle of their iconic battle on Planet Namek, and at the very end of the previous chapter, Goku became a Super Saiyan for the first time in Dragon Ball history. So this chapter shows Goku actually using his unlocked Saiyan form for the first time, and it’s as epic as it sounds. Earlier in the fight, Frieza had a clear advantage over Goku, but after Goku successfully made the transformation, the tables turned in a profound way. In fact, Frieza gets so frustrated that he screams at Goku asking what kind of being he really is, to which Goku replies, “I’m a Saiyan. Sent from Earth to defeat you. The legendary warrior, with a pure heart awakened by rage”. At this, Frieza only smiled and said, “”A pure heart,” you say… No wonder Vegeta couldn’t pull it off…”.
In this chapter, both Goku and Frieza confirm that only someone with a pure heart who allows rage to carry them to new levels of power can reach Super Saiyan, and that person is not Vegeta. Vegeta uses rage on a regular basis to push himself to new heights, and the sins of his past are simply too great for him to ever be considered ‘pure of heart’ no matter how remorseful he becomes. In fact, the original parameters of becoming a Super Saiyan actually better explain why it was considered a legendary form within Saiyan culture. No Saiyan had a pure heart in the Dragon Ball universe as they were all bloodthirsty, ruthless planet conquerors. It’s no wonder the Saiyan race didn’t think Super Saiyan was an attainable transformation, none of them met the original criteria. It wasn’t until Goku, someone raised away from the murderous violence of the Saiyan culture, who was good enough to reach this all-powerful Saiyan form.
Even though the original lore surrounding Super Saiyans made the form a bit more exclusive and relied on someone’s heroic standing as opposed to just their raw power, that entire idea was thrown out the window the second Vegeta was able to unlock the transformation after something as simple as intense physical training. However, despite what happened later in the Dragon Ball series, Vegeta would originally never have been able to unlock Super Saiyan, no matter how badly he wanted it.