Picard: "... the Enterprise crew currently includes representatives from thirteen planets."
A crew of over a thousand aboard the Federation flagship, and there are people from just thirteen planets? Not even thirteen Fed members or thirteen races, but just thirteen planets? Let's see, Earth (several), Betazed (Troi), Luna (Crusher, not really a planet), Qo'noS (Worf), Omicron Theta (Data) and the Bolian hairdresser make for six, so there just seven more. I don't believe Ensign Ro was aboard yet when Picard made his statement to Worf.
But in universe, it might be a combination of:
- humans being the most numerous species in the Federation

Okay, but a majority?
- humans being the most interested to serve in Starfleet

T'Pol claimed during Enterprise that most Vulcans aren't really all that interested in exploration for it's own sake. Other Federation races might be old home bodies. Others still might have trouble with Starfleet (supposed) military aspects.
- there are plenty of aliens that look just like humans

Kind of goes against Picard statement, even with the similarity in appearances, just 13 planets.
- we've only seen a very small part of Starfleet

In addition to our hero ships, we've seen a fair number. Still there has been a belief for decades among fans that Starfleet operates Starships with non-class M environments, water, ammonia, fluoride and others.
- it's possible Starfleet practices some measure of species separation, for practical reasons

Would seem to be outside of the Federation's diversity thing, although the above might apply.
