The tragedy of Star Wars lies in its "what ifs?" as a saga fond of parallel storylines often results in inevitable devastation. Perhaps one of the biggest and most frequently questioned possibilities is that of Anakin's training. While Obi-Wan did the best he could, things could've turned out much differently had Qui-Gon survived Darth Maul's attack in Star Wars: Episode I - The Phantom Menace. By Obi-Wan's own admission in Star Wars: Episode III - Revenge of the Sith, he was like a brother to Anakin. What Anakin needed, however, was a father figure and that was a role Qui-Gon could have filled.
By all accounts, Qui-Gon would likely have done a better job of keeping young Skywalker on the path of the Light Side, thanks to Qui-Gon's own more liberal interpretation of the Code and his natural compassion for outsiders. Anakin was nine years old when he arrived at the Jedi Temple and was flush with his own anxieties and a lifetime of traumas. Qui-Gon's calmer and wiser demeanor probably made him better equipped than the younger, more impatient Obi-Wan to understand Anakin and help him work out his emotions in a healthy manner.
Perhaps Anakin could have grown up to be one of the greatest Jedi Masters, eventually sitting on the Council as he so desired. There is even new canonical material suggesting that, with no ill will toward Obi-Wan, Qui-Gon likely would have been a far better fit for Anakin's emotional needs. The 2021 novel, Skywalker: A Family at War even says as much:
"Had Qui-Gon survived and Maul been vanquished, Anakin would have been raised under the watchful, calm tutelage of a seasoned teacher. Although the two would likely have had their disagreements, Qui-Gon’s compassion for the former slave might well have brought about a very different outcome... At the very least, he would have empathized with Anakin’s restlessness with the strict Jedi Code, offering solutions beyond the scope of Obi-Wan Kenobi’s regulation-driven mind... In either case, the predatory Sith Master Darth Sidious may well have had a more difficult time manipulating young Anakin’s future and twisting his many natural gifts into perverse, unrecognizable versions of themselves."
In this regard, Anakin likely would have grown up as a relatively well-adjusted Jedi. With Qui-Gon keeping Anakin free from Palpatine's influence before and during the Clone Wars, Anakin might never have fallen and become Palpatine's apprentice. He could have had his darker and more impulsive thoughts reigned in by an older master.
Qui-Gon also might have been able to help Anakin accept and work through even his most complex emotions, including his romantic feelings for Padmé. While Obi-Wan admitted his own feelings for Duchess Satine in The Clone Wars, he was very adamant that he could never go against the Jedi Code, no matter his own inner turmoil. Conversely, in the Star Wars Legends Jedi Apprentice series, Qui-Gon established his own romantic relationship with his friend and fellow Jedi, Tahl. They both acknowledged those feelings and agreed to weave them into their own Jedi commitments. Anakin needed an understanding mentor in this situation, and even if Qui-Gon's relationship with Tahl is no longer canon, it shows that he would have been better equipped to help Anakin channel his love away from fear-based attachment. As it stands, Anakin's selfish fear of Padmé abandoning him was a huge tipping point in his descent into darkness. With a healthier relationship established, things may not have advanced as quickly as they did and Luke and Leia might never have been born.
However, Anakin not falling to the Dark Side could've had some devastating consequences for the Star Wars galaxy. If Anakin had remained a Jedi and kept his distance from Palpatine's machinations, then the Sith Lord would've had to find another apprentice. And therein lies the problem. A different apprentice may not have had the same capacity as Anakin to be redeemed in such a powerful way. Anakin was only able to find that kernel of goodness still inside of him because of his son, Luke, who his master was going to torture and kill in front of him. Another apprentice might not have had loved ones to spur them to turn on Emperor Palpatine and fulfill that ultimate prophecy.
Moreover, the Empire's rise was inevitable and keeping Anakin out of Palpatine's clutches would not have prevented the Emperor from coming into power. Long before Skywalker, Palpatine had already put the pieces in place to raise the Clone Army and had Count Dooku as his insight into the Jedi Order. If Dooku never met Anakin, he might not have been executed and could have continued assisting Palpatine's takeover. Palpatine may still have eventually traded Dooku in for a newer apprentice, but nothing would have hindered his rise to power.
Had Qui-Gon trained Anakin and kept him far from Palpatine, Anakin might have eventually died in the Clone Wars and been completely unable to fulfill any Chosen One prophecies. He could have died an honorable death, but nothing more. Under Qui-Gon's tutelage, Anakin would have grown up to be the good Jedi and good man that both Qui-Gon and Obi-Wan knew him to be. But because of that, Palpatine would have been forced to find and train a different apprentice, one who wasn't as strong in the Force as Anakin but who also would never betray him, kill him and destroy the Empire from within.
Ultimately, Anakin's destiny and duty as Star Wars' Chosen One depended on him turning to the Dark Side. Without that story arc, the Empire could've continued to rule and Palpatine may have not been defeated. Though Obi-Wan tells Anakin after their epic duel on Mustafar, "I have failed you, Anakin," this was exactly how events needed to unfold. The Force was always out of balance, and Anakin's tragic destiny seems to have been the only way to achieve that balance. Though the outcome carried a great cost and Anakin's descent into the Dark Side is heartbreaking no matter what, all of it enabled him to fulfill his destiny as the Chosen One in the end.