Let's not forget Kirk's reference to the Earth Federation in "Friday's Child."
I initially misinterpreted your comment but it brings up a distinction that I think is worth discussing. Note you said Starfleet is still a human organization. I initially read that as "earth" organization and I disagreed with that because early on the operating organization is presented as UESPA. But after thinking about it I agree that Starfleet is a Federation organization that is primarily human; while UESPA is the Earth space organization that is also human, obviously.
Then JtB established that the Federation is in fact mutli-species, but it comes off as a rather loose political alliance between sovereign states, each maintaining their own military in the same way Germany has their own army despite being part of NATO and the EU. Starfleet, then, is part of the Federation, but still a human organization (Spock being a special case).
I initially misinterpreted your comment but it brings up a distinction that I think is worth discussing. Note you said Starfleet is still a human organization. I initially read that as "earth" organization and I disagreed with that because early on the operating organization is presented as UESPA. But after thinking about it I agree that Starfleet is a Federation organization that is primarily human; while UESPA is the Earth space organization that is also human, obviously.