I keep finding Akira annoying. Maybe realistically great many high school kids are like that: they don't want to take responsibility for anything, aside from their own hobbies and schoolwork. But Akira actually did save a classmate from the streets, so how could he be a person who doesn't want to deal with anything extra in his life? Yet in practice he only cares about his own transfer, otherwise he may cordially keep her company, but makes damn sure he won't give any input, making Aoi feel like no matter what happens to her, it has got nothing to do with him. How can such an MC work in a romcom?
You asked for too much responsibility from him. He's still a high school student. He doesn't have his own income, so he can't just force her to live with him when there's a family member that can take her (for now, let's set aside whether the dad is evil or not). That's why their focus was to find her grandma.
And he was definitely wasn't someone "who doesn't want to deal anything extra in his life". Nor did he only care about his own transfer. Nor did he not care about what happened to her.
Not only he helped shelter her, but he also helped make her social life better. He cooked for her, he helped her choose clothes, many things.
That's already beyond the responsibility of a classmate. What's more do you expect from him?
Now, if the dad is actually evil and/or she doesn't want to live with the dad, then it's on her to make the decision. Again he can't just force her.
Btw about the transfer, I understand his dilemma as someone whose family is heavily family oriented too. It's not that easy to say you want to live separately from your family.
Also keep in mind that the transfer was decided before the school started, way before he saved her. Not only that, that house isn't his house, but probably his parents'. If he doesn't want to move, his parents will need to pay two house of worth or have him rent somewhere. Unless he's planning to work, he doesn't have much freedom. But that also means another responsibility.
So yeah, it's not easy.