Alice's brother is never actually seen for at least two reasons. The first relates to the theme of distance and the second relates to the theme of self-revelation.
Aside from literally being distanced from Humphrey, as he began leaving home when he was twelve ("Humphrey was less and less at home..."), Alice is also metaphysically distanced from him as she forgets she has a brother: "Asked whether she had brothers and sisters, Alice had to remind herself she had a brother."
Humphrey thus illustrates the distanced situation Alice lives in: she is distanced from her ideals, her family, her hopes, and from any sense of home. For instance, she is a Communist yet all her contribution is in the kitchen as she keeps the "amazing soup pot" filled and feeding the multitudes of squatters. In another example, she is repeatedly asked to vacate--to be distanced from--her one sanctuary, her room:
They took my room away from me, just like that, as if it wasn't my room at all ... "Alice, you'll just have to give up your room again."
Humphrey also act as the author's stylistic vehicle through which Alice shares her sincere thoughts about her life and experience. For example, after recalling how Humphrey had "drifted away, as she had done later," she reflected that she "had not thought of this for years," then it is reveled that "She was, quite simply, dissolved in grief because of ... what she had been remembering as she stood there on the pavement."
If Humphrey were to appear in the story, his role and Alice's distanced isolation would be far less effectively rendered. So this is why he doesn't appear: the author employs his character as a stylistic device for communicating certain information and certain representations.