The problem with Sybok is his blood relation to Spock isn't of fundamental importance to the character. Make him Spock's long-lost childhood friend and the story is mostly unchanged. Moreover, it's awfully late in the game to be introducing long lost relatives of the principal characters. It's true that Spock can close himself off to Kirk at times during the television series (waiting painfully long to acknowledge that Sarek is his father in "Journey to Babel," for example), but by this point it stands to reason that the existence of a sibling would have slipped out between such close friends. Hell, McCoy had Spock's mind in his head for a while--it stands to reason that at least he would know.
Your other examples aren't really the same thing. It stands to reason that McCoy would have a father, and given his age, that his father would probably be dead. That the circumstances were only revealed at this point isn't at all surprising, since McCoy himself has repressed this part of his past.
Picard going home to visit with family isn't the same storytelling trope. He spends much of TNG closed off about his past, and as we find out in the episode, he and his brother are not particularly close. No surprise that he wasn't mentioned until that point.
Worf's adopted brother was mentioned, and he was mentioned early--in the season one episode "Heart of Glory."
Finally, Data...while I'll grant that there's a bit of a credibility issue at a certain point (how many Soong Type Androids are there, really!?) this at least gets a bit of a pass because Data himself didn't know about his "family members," which makes their lack of mention rather logical.
I guess we have to agree to disagree here. Spock not telling anyone about a half-brother who also betrayed the Vulcan way of life is perfectly reasonable to me.
Kirk and Spock are friends, yes, but not the type of talking-about-their-family-relations-friends. Kirk might tell Spock, but Spock would never tell Kirk, that's simply how the characters are.
I have various close friends who don't know anything about my family, nor do I know anything about their family. But we'd die for each other.