USS Einstein wrote:
I.E. 300 years of immigration mean there are probably thousands of alien species, even from beyond the Federation, living on Earth.
Good point. One thing that ST and its fans all too often forget is that species identity doesn't automatically correspond to political or cultural identity. A member of the Andorian species born and raised on Earth would be a Terran by nationality and culture, and a human born and raised on Vulcan would be a Vulcan citizen. But the shows always simplify things for the audience and make characters act stereotypically based on their species. Worf was always the ultimate Klingon even though he'd been raised by humans and spent most of his life on Earth. Although we did get some rare exceptions, like Jono/Jeremiah Rossa from "Suddenly Human" and Rugal from "Cardassians." But these were always treated as anomalies and the characters' default reaction was that they should be with "their own kind" instead.
It's another thing JJ Abrams may have got right - showing aliens in bars in small town Iowa - having species that might not even be Federation members in Starfleet uniforms.
Being an organization without prejudice, there is no reason a species from some distant globular cluster, who had to travel for 30 years to reach Federation space, can't sign up to Starfleet.
Also ENT did this right, with Denobulan residents, medical exchange programmes, etc. Probably Draylax, Trillius Prime, Tellar, etc, all have traders regularly visiting even in the early days of Earth's warp era.