Shinpi doesn't think that Kitty being the Otokage is in their interest.

For Shinpi, it's a choice between actively backing Jirou's bid and staying completely neutral. If Ameoku was actively cheating in the election, that would tip the scales against her even if Jirou hadn't earned his support yet.

Though, if you want an actual fight with her... The idea that she gets bought cheating and tries to take the title by force leading to a fight works.

Actually, I kind of like the idea of Team 3 and affiliated characters fighting her at once and managing to overcome her superior skill and power with tactics and numbers... In public, which discredits her strength.