Perhaps that's the point?
He is to Picard what The Joker is to Batman -- pure, unrestrained evil (who just happens to possess godlike powers).
He's the living embodiment of Lord Acton's maxim, "Power corrupts. Absolute power corrupts absolutely."
At no point did we witness any Q exhibiting "pure, unrestrained evil." I await the moving of the goalposts.
Not a Q fan. Thought he stuck out like a sore thumb on TNG
How so?
Godhood was a topic touched on (if not explored) in every previous
Trek incarnation. We had what Mitchell and Dehner "mutated" into in "Where No Man Has Gone Before." "Who Mourns for Adonais?" had Apollo. There was Trelane and his parents in "The Squire of Gothos," the Organians in "Errand of Mercy," and the pinwheel thing in "Day of the Dove." There was the entity of Delta Theta III in "Bem," and there was V'ger in TMP. Perhaps there were other preexisting godlike beings that I didn't mention.
It's hard for me to see Q as thematically at odds with the premise of
Star Trek, assuming that a being at odds with the premise of
Star Trek broadly is what you were getting at. OK, in fairness, if there is any distinction between the Q and the other previously mentioned godlike beings, at least generally, it is in that Q is not unmasked as an undivine but godlike being. That would be in contrast to, say, Trelane and Apollo.
However, the subject of where the Q lie on the spectrum of humanity's possible future development was addressed in "Hide and Q" [
http://www.chakoteya.net/NextGen/111.htm]:
RIKER: Aeons. Have you any idea how far we'll advance?
Q: Perhaps in a future that you cannot yet conceive, even beyond us. So you see, we must know more about this human condition. That's why we've selected you, Riker, to become part of the Q, so that you can bring to us this human need and hunger, that we may understand it.
That would seem to come pretty close to implying that the Q are not divine.
