@Starbright
I.. don't think that's his purpose.
His whole character motif is the fact that he doesn't like getting involved with people. The reason he doesn't like getting involved with people isn't because of some personal trauma or whatever though. He just likes peace and solitude. Himari wants to get involved with people, but she stops herself. She might've made a social mistake back in her old town, and understands that family is the only bond that can't break... so she gets close to her onii-chan.
Character arc wise, the story is shaping up to be something like this I'm guessing. The older brother who's a shut-in won't have much social experience (they've hinted at this with Himari getting dressed and the way he tried to handle the gal's manga situation.) Himari who's socially outgoing and all that is going to get involved in something and get emotionally hurt. Older brother's going to realize that he can't help her because he doesn't have the skills or ability even though by that point he'll want to, since he'll be close to Himari. It'll show both of their weaknesses from their social views and bring them closer to each other. Older brother will learn to value social skills and social interaction, while Himari will learn that she doesn't need to be a people pleaser and that she's allowed to be selfish.
Romance wise, I do see a pretty complicated picture forming as the story goes on. The only thing limiting the older brother from being popular is a desire to be social. The manga's shown him to be extremely attentive, kind and direct when he needs to be. All that's stopping him from being popular is a desire to be a part of other's lives. I think once Himari gets him out of his shell a bit, he might get involved in a bit of a love triangle.
The lesbian's going to chase after Himari, and I think the manga's going to turn it into a lesson. Himari is most likely straight, but considering how stupid selfless she is, she's going to have a hard time reacting to the lesbian's feelings.
Lots of good potential arcs here.
Only characters I don't have any idea what they'll do with is the class president and the friends himari made this and last chapter.