Humanity isn't on trial, just Picard.
It's really quite important to note that it wasn't Q's idea to hold a trial in the first place. He was just riffing off what Picard said during their "Captain to Captain" conversation earlier in the episode.
PICARD: (interrupting; angry) No! The most dangerous 'same old story' is the one we're meeting now! Those who go on misinformation,
half-information, self-righteous life forms who are eager not to learn
but to prosecute, to judge anything they don't understand or can't
tolerate.
"Q" (21ST CENTURY): What an interesting idea. Prosecute and judge?
As such, the selection of crewmen is largely driven by those that Picard surrounds himself with, his co-conspirators as it were.
When we finally see the latter part of the "trial" in the show's final episode, it's not the crew that are put to the test, only Picard.
Q: You just don't get it, do you, Jean-Luc? (leans in to him) The trial never ends.
He smiles patronizingly.
Q: (continuing) We wanted to see if you had the ability to expand your mind and your horizons... and for one brief moment, you did.
PICARD: When I realized the paradox...
Q: Exactly. For that one fraction of a second, you were open to options you'd never considered. That's the exploration that awaits
you... not mapping stars and studying nebulae... but charting the
unknowable possibilities of existence.
