From the perspective of three generations, he is undoubtedly an elder like his grandfather and an idealized elder ruler. If, as the conspiracy theory says, Kakashi, as a direct disciple of four generations, relies on his own wisdom, how can he repay the three generations righteously? Whether these three generations abdicated voluntarily or not, the successor must be young, potential and prestigious because of his age, so this person can only be Namikaze Minato, and no one else has this ability. Why? It depends on the historical process.
When did the third generation abdicate, the third ninja war? So who is Konoha who made the third Ninja War famous and shocked other countries? This is Namikaze Minato. Other orochimaru also live in harmony with Tuanzang. One of the purposes of selecting four generations from three generations is to prevent the shadow of the influence of the group. Although orochimaru is his follower, there is no doubt that he has been eliminated. Jiraiya, first of all, he had no intention of Huo Ying, and then in the third Ninja War, he didn't take part in the battle at all. In the eyes of young people, he has become a "legend" and is out.
Because the plot needs it. When four generations died, there were only three generations of partners. They can't be decision makers, because three generations have not died, and they must agree to decide who is the shadow. Their best choice is of course three generations.