It was an American show intended for an American audience so of course it's values reflected "American" ones. Which is a different thing than the UFP being an "Human Empire". Humans were used out of financial necessity not in any attempt to send a message.
Then they shouldn't have bothered giving them a multinational crew to begin with. All it did was send the message that the "silly foreigners" had realized the "error" of their lives and surrendered to American culture in the future. And even then they were subservient to a White American man.
What show did you watch? Scotty, Chekov and to a lesser extent Uhura were all proud of their non-American backgrounds. We also saw people of color in positions of authority in the show.
So show me an example of a character admitting the errors in their own culture and surrendering to American culture? An on going theme of the show is accepting what is different: The Horta, Balok or even finding common ground: The Balance of Terror. So I gain I must ask, what show were you watching?
The reception scene in "Journey To Babel" is probably more representative of what the Federation is than the crew of the Enterprise. We see a wide range of species there. Even the ones in funny clothes and wigs are meant to be non-humans. These are the people who make the serious decisions for the Federation not some cabal of humans.
It supports that the Feds are willing to maintain a pretense that they're include their weaker partners in their debates. But the TOS Movies clearly had everything be Human dominated and Human oriented even when not necessary or budget-mandated.
Heck, it's called the "Earth Federation" in one episode.
How does it support this idea? Show me something in the episode that proves this.
Even the TOS movies had budget limits. Having alien make up that is front and center is a different cost than background aliens. Though in TUC the President of the Federation is a non-human.
Star Trek is a TV show. One that was evolving as it was made. In the beginning the Enterprise was an Earth ship working for the UESPA and Spock was a Vulcanian from the planet Vulcanis who had a human ancestor. One stray piece of dialog proves very little.