I would argue that Deep Space Nine is the exception. While there are plenty of dysfunctional family moments and family related tragedies over all the familial relationships in the show are strong and emotionally deep, most especially, in my opinion, the relationship between Capt Sisko and Jake.

Although DS9 dealt with your point about friends vs family very explicitly in an episode where O'Brien struggles with the idea that he feels closer to his best buddy Bashir than to his own family. I think that of all the Star Trek stories DS9 was the most aware of family issues, something that was surely helped by the fact that it primarily is set in one place. In DS9, the characters have a home.