Disagree. (All of the following numbers are from my own memory, occasionally using Memory Alpha to confirm a name.)
TOS:
5 Human characters, all Earth-Born:
Kirk - American
McCoy - American
Sulu - American
Uhura - African (Adjective chosen by analogy to American, since both nations are ‘USA’, where the ‘A’ is the continent.)
Chekov - Russian
1 Alien: Spock.
Core cast of 6, 3 American, each of the others from different nations, one of whom is non-human.
TNG:
3 Earth-Born human characters:
Picard - French
Riker - American
LaForge - African Confederate
2 Aliens:
Worf - Klingon, born on a colony world, raised on Earth, in St Petersburg, Russia
Data - Android, built on Omicron Theta
2 known non-Earth-Born humans:
Yar - Tarkanian
Dr Crusher - From Luna
2 humans of unknown birth:
Dr Pulaski
Wesley Crusher
Core cast of 9, 2 American, 2 of unknown extraction, 5 others from 5 different nations/worlds.
DS9:
4 Earth-born humans:
Ben Sisko - American
Miles O’Brien - Irish
Keiko O’Brien - Japanese
Julian Bashir - Not conclusively known, but likely English
7 or 8 Aliens:
Jadzia Dax/Ezri Dax - Trill
Odo - Changeling
Kira - Bajoran
Quark - Ferengi
Nog - Ferengi
Rom - Ferengi
Worf - see above.
1 human of unknown extraction:
Jake Sisko (circumstances suggest he was space-born).
Core cast of 11 or 12, depending how you count the Daxes, 3 Ferengi, 1 or 2 Trill, one of unknown birth, each other major character from a different nation/world.
Voyager:
3 Earth-Born humans:
Janeway - American
Kim - American
Tom Paris - Not entirely sure, but I think American
7 Aliens (including hybrids):
Tuvok - Vulcan
Kes - Okampa
Neelix - Talaxian
Ceska - Cardassian, masquerading as Bajoran
Torres - Human-Klingon hybrid, born on Kessik IV
7 of 9 - Borg, born Human on Tendara colony
Naomi Wildman - Human/Ktarian hybrid, born aboard Voyager
1 non-Earth-Born human:
Chakotay - Native American, born on an unnamed colony.
Core cast of 11 3 American, each of the 8 others from a different nation/world.
Enterprise:
4 Earth-Born humans:
Archer - American
Tucker - American
Sato - Japanese
Reed - English
2 aliens:
T’Pol - Vulcan
Phlox - Denobulan
1 known non-Earth-Born human:
Mayweather - born and raised on a freighter.
1 character of unknown extraction:
Hayes.
Core cast of 8, 2 American, 1 unknown, each of the other 5 from a different background.
Ignoring the aliens, the counts go:
TOS: 5 humans: 3 American, 2 other.
TNG: 7 humans: 2 unknown, 5 from different backgrounds.
DS9: 5 humans: 1 unknown, 4 from different backgrounds.
Voy: 4 humans (5 if you count 7): 3 American, 1 (2) other.
Ent: 6 humans: 2 American, 1 unknown, 3 other.
Multiculturalism rating (to the extent that the fairly generic humans can count as such), in descending order:
Overall: DS9, TNG, Ent, Voy, TOS.
Human-only: TNG, DS9, Ent, TOS/Voy (tie, or TOS slightly edging out Voy, depending on count).
Human/Alien ratio: DS9, Voy, TNG, Ent, TOS.
These core casts didn’t have those numbers all at once (Save TOS, once Chekov is added), due to cast changes. I considered including Nurse Chapel and Yoeman Rand for TOS, but ultimately decided they were both glorified guests.
I’m going to get a rep for ridiculously analytical Star Trek posts, aren’t I?