Shino doesn't realize she's popular...
I think the tsundere kohai (Koizumi) is like Nozomi's gender-nonconforming friend (Heidi) in that both are set up to be pivotal characters if and when the sexual tension in this series finally snaps. And they're flavor if it doesn't. Koizumi's entire life is shaped by suddenly being forced to take care of her younger sister, and being rigid and fiery about it. She is a sisterhood fundamentalist who may be attracted to Shino, which is an explosive combo.
For instance, if Shino is outed to Koizumi as romantically attracted to Nozomi, a big sis figure and the teacher of the Koizumi's little sis, Koizumi will definitely be grossed out by the messed up sisterhood and age gap. Maybe she'll try to prevent her (platonic?) crush from doing something with Nozomi. Koizumi also may be used to verify super-dense Shino's orientation. Koizumi is fireworks prepared for if Shino is gay.