There used to be something like that, and I'm not sure whether it still exists. My father's family housed an exchange student, a Black girl from another part of America, and later a girl from Norway (I think). Of course this wasn't specific to cultural exchange within America in particular, but it wasn't to the exclusion of American students.
However, I must admit I may be wrong in my interpretation of this, and now I want to ask my dad again next time I see him.
It is a great idea, nevertheless.