Irrespective of Dragon Ball Super. That undeniable importance and the understanding that the franchise really has no choice but to answer this question place quite a bit of focus on Goku's character and what could have possibly happened to him and his ability to tap into Super Saiyan 4 on his own. But Vegeta's incredible development is unquestionable.
Even before Daima, Vegeta was easily one of the franchise's most complex characters because of how much he changed from a heartless villain who only cared about himself to a begrudging ally and family man. But an argument can be made that Vegeta undergoes much more complex and nuanced changes in Super than he ever did in DBZ. And while Vegeta may have achieved Super Saiyan 3 in Daima, that isn't what makes his actions in the series so pivotal when contrasted to the later events of Super. It's what he calls his Super Saiyan 3 form.
Dragon Ball Daima Positions Vegeta's Name for Super Saiyan 3 as a Punchline
Is Ultra Vegeta 1 More Than Just a Way to Win an Argument?
Near the end of Dragon Ball Daima episode #20, Vegeta berates Goku for hiding Super Saiyan 4 from him and then belittles Goku for achieving another level by referring it to as being like "a bargain sale for Saiyans," to which Goku deflects by saying that Vegeta did the same with Super Saiyan 3. This observation obviously touches a nerve with Vegeta who then says that he didn't achieve Super Saiyan 3, but "Ultra Vegeta 1."
In this case, Vegeta is obviously trying to protect himself from being blamed for doing the same thing that he had just poked fun at Goku for doing. He is therefore trying to separate himself from what he did as something that did not involve getting "a bargain sale" on Super Saiyan transformations like Goku. On the surface, this might feel inconsequential or just a funny way of Goku catching Vegeta being hypocritical and calling him out on it, but it actually has a lot of meaning when compared to the type of mentality Vegeta espouses in Super.
Ultra Vegeta 1 Is a Direct Reference to Ultra Ego
What Begins as a Joke in Daima Becomes a Foreshadowing in Super
In Super, Vegeta becomes obsessed with suring Goku his own way, so that he stays out of Goku's shadow. Although it happens more in the manga, Vegeta's obsession in the anime starts when Goku begins pursuing Ultra Instinct. Vegeta constantly refers to it as Goku's technique and refuses to learn it himself, which is mainly why he tries to train under Beerus to master Destruction. Apart from the concession Vegeta makes when he ironically goes to Yardrat as Goku did in DBZ, Vegeta's attempts to differentiate himself from Goku in Super now hearken back to this otherwise humorous argument in Daima.
In Daima, it begins as a way for Vegeta to win an argument, but after Goku achieves what's later referred to as Ultra Instinct -Sign- during the Tournament of Power, it becomes an all-out mentality that shapes Vegeta's code as a warrior. The greatest example of this takes the form of his very own transformation that Vegeta partly names after himself, as he did with Ultra Vegeta 1 this time, it's Ultra Ego. Not only does Vegeta's Ultra Ego form flip the concept of Ultra Instinct, but it is based on who he is as a Saiyan, hence the word "Ego."
Dragon Ball Daima Ends in Reference to Where Super's Original Story Left Off
Vegeta Could Very Well Be Creating Ultra Vegeta 2
In fact, that's where the actual Super story leaves Vegeta. Before the series took an odd detour by adapting Dragon Ball Super: Super Hero, the latest truly original installment of Super, chapter #93, includes Vegeta actively trying to invent another type of technique on his own through meditation. Despite the fact that Vegeta is essentially creating his own version of Ultra Instinct instead of Ultra Ego, it's noteworthy that his latest conquest is in pursuit of that very mindset that began taking shape at the end of the franchise's latest project, Dragon Ball Daima.
Although the bulk of Dragon Ball Daima revolves around Goku, especially his Super Saiyan 4 transformation, it's telling that his story still doesn't align with the later events of Super when Vegeta's story is the perfect jumping off point for whenever Dragon Ball Super decides to continue.