By being "pure" Goku's hearts desires were made unshakeable, and since he's a Saiyan his main heart's desire would be to fight and improve without any outside thoughts to hinder his desire to improve unlike regular non-pure Saiyans. His purity was made concrete by his upbringing. Master Roshi's teachings relates perfectly in conjunction with Goku's purity and not letting the idea of statuses cloud one's mind from their work and how one should work purely to improve oneself in order to attain health in both mind and body and feel more fulfilled with the achievement of improvement alone.
Vegeta embodies the negative effects that come with not following Master Roshi's teachings, (i.e Not acquiring the right mindset in training) hence why he couldn't catch up with Goku. Although Vegeta is more gifted than Goku he allowed himself to be more concern with outside thoughts such as social status and money (Mainly social status) which hindered his great potential. This applies greatly to real life situations, people would focus too much on besting others rather than besting themselves which ends up backfiring at them since they'd either feel unfulfilled with the improvements that were gained via their obsession. The best example of this in DBZ was in the Cell arc when Vegeta couldn't achieve Mastered Super Saiyan like Goku despite being a better genius on paper because he allowed his anger towards not being the best consume him and could only aim for the forced variation of the MSSJ known as the grade forms (Ultra Super Saiyan), which had negative effects of stamina consumption and speed decrease, similar to how athletes who are unsatisfied with improvement for improvement sake rely on forced methods such as steroids to get better, which in the end can led to side effects such as anger and depression, which Vegeta had in the end of the Cell arc because of the mindset he placed on his training.
This is why it was necessary within the story of Z for Vegeta to be inferior to Goku, it's because of the message it brings. Vegeta should have been happy after Goku died in the end of the Android arc since he surpassed the Super Saiyan and Frieza's empire but, like workers in real life who follow the wrong mindset that isn't Master Roshi's teachings, he ended up feeling sad and depressed because he allowed his anger to be his guide rather than focusing more on self improvement.
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