The relationship between art and culture is a messy one. "The Weary Blues" can be read as a defense of blues music as art, but it is also a defense of itself as art. Langston Hughes spent a lot of time trying to write poetry that would be accepted as art, but not at the expense of abandoning his culture. One of the blues lyrics reads "Ain't got nobody but ma self." Is an identity all you need to make art? Go onto Facebook, and you can see how your identity includes the music you listen to, the authors you like, the way you talk, and the way you talk about people. If all those things come from your culture, what are you?
Art comes from the culture it defines, and the culture is defined by the art it makes.
The differences between the speaker of the poem and the blues singer are their ways of expressing themselves.