As the namesake of Akira Toriyama's massively popular Dragon Ball franchise, the mystical artifacts are capable of some truly stupefying feats. From bringing the dead back to life to restoring entire universes, the various Eternal Dragons make the impossible look easy. And though there are many wishes that glaringly have yet to be made, one has to wonder why Goku and Vegeta have never used the Dragons Balls to resurrect the Saiyan race after they were wiped out singlehandedly by Frieza.
While the Super Dragon Balls are capable of restoring the multiverse, even Earth's Eternal Dragon, Shenron, can resurrect billions -- as seen when it restored the planet from Majin Buu's devastation. With Vegeta and Goku speaking of Saiyan pride throughout the entire series, it's a wonder that they haven't used the Dragon Balls to restart their race and reform their home planet following its own destruction, with the only survivor living because they were off-world at the time. However, Goku and Vegeta's reasons for bringing the Saiyans back is eluded to by both over the course of Dragon Ball Z.
Arriving on Earth as an infant and losing his original Saiyan mental programming after being dropped on his head, Goku never really got to know his Saiyan heritage. Goku's first exposure to Saiyan culture was through the debut of his long-lost older brother Raditz, who immediately proved to be a formidable villain, resulting in Goku's first death.
Despite this bad introduction, Goku did form his own sense of pride for his Saiyan heritage, specifically when he took the chance to avenge them by confronting Frieza. However, Goku later expressed to Vegeta that the two of them could set aside their petty rivalry and form a new race that combined the best elements of humanity and Saiyans through their own children, convincing Vegeta to use the Potara earrings to fuse with Goku into the composite warrior Vegito to fight Majin Buu.
Vegeta similarly has never expressed a visible interest in resurrecting his fallen race, initially seeking the Dragon Balls to gain immortality for himself rather bring anyone else back from the dead. This disinterest in a full-on revival of the Saiyan race was apparent when Vegeta first learned that his homeworld and race were wiped out as a child, barely hesitating as he continued to conquer worlds in service of Frieza. This may be due to the Saiyans being a warrior race, seeing defeat as a deep dishonor, meaning Vegeta likely felt that his fallen brethren were not worthy to resurrect, outright dismissing the possibility of reviving Raditz with the Dragon Balls when Nappa suggested so in passing after Raditz's death.
Goku can't even remember to use the Dragon Balls to resurrect King Kai, even despite the god's very consistent, very irritated reminders that he should do so. And with Vegeta not being one to look back, especially at those that fail to impress him, the Saiyan race is likely dead and gone for good in Universe 7. Fortunately, a variation of the Saiyans continues to thrive in the alternate reality of Universe 6 -- no thanks to anyone in Universe 7.