Here’s my theory on why Vegeta didn’t go Super Saiyan 3.
Why couldn’t Vegeta turn into a Super Saiyan 3?
It’s because he actually didn’t want to. He understood that he’d get mocked for continuing to copy Goku. Vegeta wants to pave his own way to power. I bet Akira wanted it that way too. He wants to have a boost that’s worth bragging about.
Trying to Copy Goku
We have to realize we’re talking about one of the most prideful Saiyans in the entire show here.
When Goku went Super Saiyan first that hurt Vegeta in a way I could only imagine.
He had his moment when he proved to reach Super Saiyan Grade 2 in the Android Saga.
It only did so much though.
Being a mirrored rival to Goku means that Vegeta’s gonna do whatever possible to pass him up in terms of power.
Toriyama could care less for Super Saiyan 3
Final Thoughts
Vegeta not turning Super Saiyan 3 is merely a minor extension of his legendary rivalry in all of anime with Goku.
RealTalkAJ 
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