The quota system was set up because of racial and eugenic concerns rather than some progressive notion of diversity. Though it should be noted that eugenics was considered progressive policy at that time. So it would be a very peculiar accident that it happens to resemble sane and forward thinking policy
As to why countries instead of races,
>The question will probably at once arise, why, if this legislation was a response to a demand for racial discrimination, was it expressed in terms of nationality? The answer is simple. As has already been shown, our actual knowledge of the racial composition of the American people, to say nothing of the various foreign groups, is so utterly inadequate that the attempt to use it as a basis of legislation would have led to endless confusion and intolerable litigation. So Congress substituted the term nationality, and defined nationality as country of birth. It is clear, then, that “nationality,” as used in this connection, does not conform exactly to the correct definition of either nationality or race. But in effect it affords a rough approximation to the racial character of the different immigrant stream
https://www.cato.org/policy-analysis/brief-history-us-immigr...