Risa

Gene Roddenberry did consider the diversity of the cast to be a big victory for representation on television. Having prominent female (in a military fleet role), African American, Japanese, Russian (and even Scottish) core characters wasn't typical in US broadcast prime time TV when TOS aired in a prime time slot. It seems like it was important to Gene to show a version of humanity that had forgotten "old" country borders.

It's worth noting that Gene claimed to have added Chekov in response Russian criticism of the show at launch, along the lines of "we were first to space, but there's no Russians on the Enterprise". Gene told the story a few times, but I'm not aware of any hard corroboration. Not that it really needs any.

And as someone pointed out - Walter Koenig has, perhaps joking, commented that his looking like a member of the Beatles was probably really why he was cast.