Of note: Cthulhu isn't a god, he's just an unusually powerful example of the Old Ones, the species that dominated the earth before humans.
The emphasis in Lovecraftian mythology is on the futility of human existence... there were dominant species before us, and there'll be others after us, our current success is doomed to be shortlived, and the end will be painful.
Actual Lovecraftian gods... Yog-Sothoth has been banished to another plane but is enlisting the help of various wizards to bring him back, which if he does, humanity will be instantly wiped out by the corrupting influence of his mere presence in our universe. My favourite, though, is Azathoth, about whom I'll simply include a quote...
“...that last amorphous blight of nethermost confusion which blasphemes and bubbles at the centre of all infinity—the boundless daemon-sultan Azathoth, whose name no lips dare speak aloud, and who gnaws hungrily in inconceivable, unlighted chambers beyond time amidst the muffled, maddening beating of vile drums and the thin, monotonous whine of accursed flutes; to which detestable pounding and piping dance slowly, awkwardly, and absurdly the gigantic ultimate gods, the blind, voiceless, tenebrous, mindless Other Gods whose soul and messenger is the crawling chaos Nyarlathotep.”
Compared to Yog-Sothoth, Shub-Niggurath or Azathoth, Cthulhu is pretty insignificant. I mean, sure, he can still drive us insane by possessing our dreams, and when the stars are right he'll come back to rule over us, but, in a universe where something like Azathoth lurks, being driven insane and eaten by Cthulhu is really the merciful option we should be striving after and hoping for.