Asking what might have happened during a monumental moment is usually bound to create a chain of events that are going to emerge in a person’s mind in several different ways since the implications that this simple question brings up can be numerous. The question of what might have happened had Anakin Skywalker defeated Obi-Wan Kenobi during their battle on Mustafar in Revenge of the Sith carries a lot of heavy consequences since one has to remember what was happening before the two decided to cross blades. Anakin had already flipped over to the dark side, but perhaps not all the way yet, and Padme had realized just how twisted the father of their children had become. He’d killed younglings, he’d helped to initiate the Jedi Purge, and there was no easy to come back from that. To be realistic, there might have been no way to come back from it at all. But just before the fight, Anakin actually Force-choked his own wife, threatening her life and the lives of the children that had yet to be born.
But getting into the battle, it’s not hard to imagine that the actual fight would go the same way no matter what since Anakin and Obi-Wan were evenly matched since Anakin was more powerful, but Obi-Wan was more experienced and far more balanced. Where the deviation would come, almost certainly, would be when Obi-Wan states that he has the high ground. Jumping up in the air at that point was one of the dumbest moves that Anakin could have made, while leaping to the embankment, well clear of the lava flow, would have been preferable. Given that he was enraged and not thinking straight, it might have been that Anakin was hoping to take out his former mentor in a flourish that would defeat Obi-Wan much as he’d dealt with Darth Maul in The Phantom Menace. The unfortunate reality for Anakin was that Obi-Wan managed to learn from each battle and remember moments that might have gone differently with one or two moves.
This time, however, Anakin’s forward movement would mean that Kenobi would have to take him head-on, and wouldn’t be given a free shot at the overconfident fighter. Imagine if Anakin manifested Force lightning through his biological hand while wielding his lightsaber in his other hand, keeping Obi-Wan pressed continually until the older Jedi, who would have to fend off both attacks, would either slip or grow tired. If Anakin could have kept his rage stoked and his attacks coordinated, he might have had a chance to utilize his greater power to wear Obi-Wan down. With Kenobi dead, either chopped in two or simply cut down, Anakin would have unleashed a new future that would have been much, much different. Not only would he try to save Padme and the children, but it’s fair to think that he might have taken his children, or rather, Palpatine would have taken his children and twisted and warped them to become the new generation of Sith. It’s possible that each one of them would have become an Emperor’s Hand, assassins that would do Palpatine’s bidding, much like Mara Jade did in the Legends canon.
It’s conceivable that Yoda and Bail Organa would have still escaped, but without Luke and Leia, hope for the future might have waned to a dangerous degree since, without the twins, the Jedi were all but dead, no matter that many of them still existed throughout the galaxy. In the current canon, it feels likely that Yoda would have spent the last of his days on Dagobah, regretting his defeat and the loss of the order. Ahsoka might have continued to fight, but there’s no doubt that her life would have changed as well. A great deal would have changed throughout the history of Star Wars had Kenobi fallen, as Owen and Beru Lars might have survived, but Han Solo and Chewbacca might have never made it out of Tatooine alive since Jabba was on the hunt for them. There are a lot of things that would have happened had Obi-Wan fallen to Anakin, and very few of them are positive, which means that Obi-Wan is essentially a linchpin to the Star Wars universe that, if removed, would cause quite a few chain reactions.
Stating that one character can cause such chaos if they’re removed feels like something that might be regarded as a kind of dramatic, but when a person takes a look at the story and realizes how vital one person or another become in their capacity, believing such a thing is far easier. Obi-Wan Kenobi is not a character that could be replaced or omitted easily unless one wanted to deal with the heavy load of consequences that would come as a result. So to be fair, the higher ground did matter just a little bit, no matter how many people might want to think that it made little sense.