"So, Kai, I know you've defeated one of the four races leaders already and you have the Code Breaker sword thing, but... step the fuck off, Girl Boss here is the new hero."
...What is this shit? Jeanne is definitely a leader and would be a driving force in uniting humanity, commanding forces, rebuilding, etc. - sure. That's definitely what she'd excel at. But... Kai is the one that killed the demon's leader. He's the one that's been the only one (outside of Rinne) that's capable of thrashing the fuck out of the enemy leaders. He's the one with the chosen one's sword... thing... whatever... So how is he not the Sid's replacement? He has Sid's fucking sword, he's the one that's defeating these foes (yes, sure, with help, but Jeanne wasn't the one to kill the demon's leader). This makes no sense.
It's not that she will be the one to save the world, it's that she will be the one they rally behind.
As is, she was already an icon in in her own faction of the rebellion. She took on the role of commander for her injured father. Everyone else was told that she was one one that defeated the demon hero. She was the one who left the senior commanders in charge of rebuilding their city cause the ones who had fond memories of the towns former glory would do a better job than her. They believe that it was thanks to her that the commander of the previous town was saved and they now have a one year armistice with the people they were afraid could attack them. And now she and her companions are going to visit the next group of rebels.
She has literally become a symbol of humanities rebellion.
That is unfortunately a very heavy burden to bare. What would happen if it came out she, he a long standing commander of the human rebellion, lied about defeating the demon hero and it was in fact done by a random person who was younger than her and not a part of the rebellion? Literally a few days after he arrived the demons were defeated. They were suffering for over a century and lost the war 30 years beforehand and a nobody did what they couldn't do in that time. It would undermine everything about the current rebellion.
Now admittedly, they MIGHT rally behind him, but do you really trust humans that much? Old men who spent decades at the top of the rebellion suddenly being questioned and their power being threatened? Even in our world things aren't that kind. They can save face and say the "Knight of Light" did it rather than a kid they literally picked up off the streets a couple days ago. If it got out, you can easily imagine the chaos and infighting it would cause amongst the people and the rebellion.
She is the hero humanity needs to follow to insure their unity. Part of that is that Kai is by her side along with Rinne and the others. Without Kai the rebellion would fail, with Kai they have a chance, with Kai and humanity united behind Jeanne things can actually change for humanity.