I didn’t put it in the post because I can’t remember the specific details and was too lazy to go reread. But when speaking to Ichika on the ship, Yagami seemed confident in his that he could’ve already expelled Kiyotaka if Tsukishiro and Ichika didn’t keep interfering with his plans. I’m unsure how they interfered with him, but Ichika doesnt even attempt to deny it. Now even if Yagami would’ve expelled Kiyotaka without intervention from Tsukishiro and Ichika, that alone imo wouldn’t make him superior. As he started from an advantageous position already (Kiyotaka not knowing who he is, and Yagami having all the information in the world about every student at ANHS beforehand). However I believe Yagami was much much much more capable than most give him credit for.