Why didn't Kenshin's master, Hiko Seijuro, come and fight Master Shishio Makoto in the showdown of the Kyoto Arc?
This is one of the many times that the Meiji government called on Kenshin to solve their problems, even though his master is as skilled as he. (This is especially true before Kenshin learned the final technique.)
Because Master Seijuro wasn't interested! He was, to put it bluntly, an introverted, misanthropic and somewhat lazy martial artist, who thought the world an unredeemable place, felt Kenshin a fool for wanting to improve society, and didn't care in the least to take down Shishio. (See particularly his interactions with Kenshin during episode 41, "The Ultimate Technique of the Hiten-Mitsurugi Style: Reunion with a Mentor, Seijuro Hiko".) To quote from the Kenshin wiki page on him:
Kenshin describes his personality as "twisted, brusque and misanthropic" ... He dislikes the complications of socialization, and hearing of the ills of society, both of which he finds annoying, and to the latter's weight, ultimately incessant and depressing. In order to avoid having to work with people, he makes his living as a pottery artist alone on a mountain (a profession that he is reported to excel at). He also comes off as somewhat lazy, professing to have retrained Kenshin to save himself the bother of having to deal with Shishio, and later on, he complains about having to protect Kenshin's friends, after the latter insists him to do so (though he does).
It's only after much cajoling that he agrees to teach Kenshin what he needs to know to defeat Shishio (episode 43, "Between Life and Death: Master the Ultimate Technique, Amakakeru Ryu no Hikameki!"), but beyond that, the most he will agree to do is to (grudgingly) keep an eye on and protect his friends, while Kenshin does the actual hard work of fighting Shishio (episode 53, "The Giant Versus Superman: Like an Arrow Shot at a Time of Despair")!
This is gonna set some people off, but the simple truth is that Hiko would have lost to Shishio.
First, Hiko's defense is not impenetrable. Even before learning the succession technique, Kenshin was able to land a hit on Hiko when his focus and motivation were at 100%. That means Shishio would have likewise been able to hand hits on Hiko.
Meanwhile, Hiko's capacity to take damage is no better than anyone else's. Yes his muscle mass gives him some protection, but it didn't protect him from the Amakakeru Ryu no Hirameki. And consider getting hit by that technique knocked him out for a full day, whereas Shishio could withstand the full force of the stronger version of the technique and keep fighting, and even Aoshi could maintain consciousness. That suggests one Guren Kaina would have knocked him out, and even Homura Dama would have whittled away his fighting strength.
All of which is to say, his build, technique, and blade give him incremental advantages over Kenshin but not so much that motivation and fighting spirit wouldn't factor in. And on those counts, Kenshin is leaps and bounds ahead, being more invested at an ideological level (caring more about what happens to the government) and a personal level (redeeming his own legacy as hitokiri), contrasted to Hiko's personality ("twisted, brusque and misanthropic") and politics (the Hiten sword must maintain its independency from factions)
All of this is set up within the narrative itself, which is why Kenshin didn't bother asking his master to help him out. Of course, protecting the weak from roving bandits is right within his wheelhouse, which is why he is willing to protect the Aoya.
Essentially it is because it is not his fight, this is the symbolic end of Kenshin's arc as an assassin. Kenshin knew this and that is why he only asked Hiko to make sure his loved ones were safe. For the story it would be boring because he would just waltz in and kill everyone in a couple minutes, maybe seconds. Hiko Seijuro is the best swordsman in this universe by far, he is superman. He is stronger, faster, more skilled and more experienced than Kenshin. Kenshin hit him with Amakakeru because Seijuro forced him to in order to teach him how to do it. The only area where Kenshin measures up is heart, he may even surpass Hiko in this.
He very well could have. However that's not the final lesson he wished to bestow. He let Kenshin do so, namely because in actuality it's partially his mechanations that caused this circumstance with Shishio in the first place. Mush like the Sith in Star Wars, Ascension to Master requires typically the student kill the master by perfecting the final technique. The master-apprentice dynamic continues to point of succession in which the apprentice graduates by successfully besting the master in a life or death struggle. Practitioners of Hiten Mitsurugi style of swordsmanship; capitulated to Maintain independence of any and all political entities, stressing highly the importance of wielding its expertise in the name of humanity; and NOT serving any political, government or institutional body. Since Shishio was attempting to overthrow the Meiji government, killing/disposing of him would be a political move (And the Hiten style Stresses it's practitioners take NO ambition to accumulate political power or change political dynamics)
imagine you inherit a power so great, then realize you have to kill a million to save a million. Hiko was right. “It is forbidden to kill; therefore all murderers are punished unless they kill in large numbers and to the sound of trumpets.” ― Voltaire
The author of the Manga stated that Hiko is too powerful and would make all encounters trival and boring.
This is Kenshin's story not Hiko's.
He obviously wasn't interested in fighting for the government. He scolded Kenshin many times and even mocked him for taking sides with the government and what it made him to be. He could definitely defeat Shishio if he wanted to.
