Yagyu taking Tsunade away naturally wasn't for something as boring as simply taking a hostage.
He took Tsunade to make the position of Hokage confusing and unstable.
Previously, Yagyu had inflicted too much damage on Konoha, and someone had to take responsibility for these events.
Based on the principle that whoever holds power bears the responsibility, the Third Hokage's position would become extremely shaky.
If Yagyu hadn't taken Tsunade, the future Fifth Hokage of the original story would likely have become the Fourth Hokage now.
In that scenario, the Third Hokage could step down, taking all the blame and using his resignation as atonement, which would largely stabilize the situation in Konoha.
However, with Tsunade taken by Yagyu, Konoha was left without a suitable candidate to succeed as the Fourth Hokage.
The original Fourth Hokage, Namikaze Minato, was now effectively cut off from the position. Neither the Third Hokage and the higher-ups nor the common people of Konoha would agree to let someone who lacked the necessary sense of duty succeed as Hokage.
As for Jiraiya, it went without saying—having lost an arm, his strength had declined, making him unfit for the Hokage seat.
Shimura Danzo was in a similar boat to Jiraiya. Also missing an arm, he could only remain in the shadows as Konoha's scapegoat king.
Orochimaru certainly had the strength and prestige to become the Fourth Hokage, but Sarutobi Hiruzen wouldn't allow it. Even if Orochimaru claimed he didn't care about Hiruzen attacking him earlier, would Hiruzen dare to believe him?
A rift had formed between the once-inseparable master and disciple.
Konoha's White Fang...
It was almost impossible for Sakumo Hatake, the White Fang, to ascend to the position of Hokage.
Although inheriting the title of Hokage didn't require blood relation, it did require a close connection to the previous Hokages.
This connection could be direct, like master-student, brothers, or father-son; or indirect, like grandmaster-student.
For instance, looking at the history of Hokages, they all shared close ties.
The Second was the First's brother; the Third was the First's student; the Fourth was the Third's grand-student; the Fifth was the Third's student; the Sixth was the Fourth's student; the Seventh was the Fourth's son and also the Sixth's student...
Other villages were similar. The Third Tsuchikage was the Second Tsuchikage's disciple and also the Fourth Tsuchikage's grandfather.
The Fifth Kazekage was the Fourth Kazekage's son, and the Fourth Kazekage was the Third Kazekage's disciple. (According to official lore, the Fourth Kazekage Rasa learned his Magnet Release from the Third Kazekage.)
The lineage between the earlier Tsuchikages and Kazekages wasn't explicitly clear, but it was certain they had close connections.
From father to son, brother to brother, master to disciple.
In short, it was a system built on bloodlines combined with master-disciple succession.
Regrettably!
Konoha's White Fang had no close connection to any of the existing Hokage lineage.
Without a close connection to the Hokage, how could he inherit the Will of Fire?
How could someone without the Will of Fire serve as the Hokage of Konoha?
Konoha's White Fang was out!
To be precise, he had never been in to begin with.
The Hokage could only be chosen from the Hokage lineage, emerging from their small inner circle.
The White Fang was not part of the circle!
What a pity!
The simple villagers and naive lower-ranking ninjas of Konoha didn't know this.
The White Fang's strength and prestige might lead a portion of the people to recommend him for Hokage.
"When that happens, maybe it will be the White Fang's death date, right?"
"After all, if the White Fang were to become Hokage, it would be equivalent to a regime change for Konoha."
Yagyu muttered to himself, anticipation rising in his heart.
Aside from these people, Mitokado Homura, Utatane Koharu, and Akimichi Torifu—the three disciples of the Second Hokage—were also qualified to become Hokage.
However, their abilities and strength were too average, and they lacked sufficient prestige within the village. The difficulty of them becoming Hokage was exceptionally high.
If a Hokage were born from among the three of them, Yagyu would be very happy.
Because... that would deal an even greater blow to Konoha!
...
Kirigakure Forward Base.
Terumi Mei sat bored on the branch of a large tree outside the Kirigakure base.
Her gaze was fixed in the direction of Konoha, seemingly waiting for someone to appear.
Genji appeared beside her and spoke calmly, "There is no point in waiting here blindly. He will return when the time comes."
Terumi Mei rolled her eyes and said grumpily, "Easy for you to say. That's the strongest ninja village in the world—Konoha!"
Genji smiled and said, "Even for Konoha, dealing with Yagyu is not easy."
"His abilities are simply too overwhelming; there aren't many methods that can threaten him."
"No matter how many ninjas Konoha has, without a specific counter to Yagyu, it's useless."
Genji looked emotional, clearly envious of the special abilities Yagyu possessed.
Terumi Mei worriedly said, "Even if Yagyu-kun's abilities are very powerful, Konoha is not to be trifled with."
"There are countless talented individuals in Konoha, and powerful secret techniques are not in short supply."
"Yagyu-kun's ability hasn't reached the level of invincibility yet. Konoha should have means to deal with him."
Genji mused, "Konoha having means to deal with Yagyu... I agree with that statement."
"However... Yagyu's strength lies not only in his special abilities. I believe he can handle it."
Terumi Mei said gloomily, "Can't we send a ninja squad to Konoha to meet Yagyu-kun?"
"When we left Konoha, he sent a clone to escort us."
Genji hesitated for a moment, then shook his head. "No! The Third Mizukage hasn't issued an order for war. Doing so could easily provoke a conflict."
"Besides, Yagyu didn't ask us to do this. We shouldn't act rashly."
Genji looked at Terumi Mei and comforted her, "You don't need to worry too much. Yagyu will be fine."
"Even if he is captured by Konoha ninjas, we can get him back through threats of war or honest negotiations."
Terumi Mei's expression suddenly changed, and she said joyfully, "I think that won't be necessary. I see him."
Genji was stunned, then delighted. "Really? Let me see!"
On the main road ahead of the Kirigakure base, Yagyu was walking leisurely toward them with Tsunade.
Genji and Terumi Mei were overjoyed and rushed over without hesitation.
Both Terumi Mei and Genji placed great importance on Yagyu.