One of the questions that many fans have been for a long time is the reason why Vegeta never managed to reach Super Saiyan 3.
SOURCE The Original Design of the Super Saiyan 3 together with the final design.
Toriyama explains that the reason is what many suspected, basically time and money since it mentions that it is very complex to draw, color and animate so a scene with the Super Saiyan 3 can have a very high cost.
So this is the reason why we did not see Vegeta, Gohan and the others reach this stage.
Previously Toriyama had explained that the Saiyan had blond hair because in the manga it would be much faster to leave them blank, with the idea of speeding up the production process.