I think family comedies can still thrive. Take Modern Family for example.
I haven't seen Tim Allen's new show, but I have high hopes. What seems to be missing is diversity when it comes to family shows.
In the prime of family TV shows (my childhood of course), you had Home Improvement, Everybody Loves Raymond, The Cosby Show, Fresh Prince, Full House, Married with Children, Malcolm in the Middle (late childhood), Roseanne, and Family Matters.
Each one of those shows brought a unique perspective of family life with its own style of comedy.
The family show has been replaced with a bunch of extended Saturday Night Live skits that feature late 20s/early 30s single people.
Not that those shows are inherently bad. A few are great.
But comedy is mostly dead on TV.
Luckily, a few stations like AMC have had the audacity to put HBO-level shows on TV. Breaking Bad, The Walking Dead, and Mad Men have all flourished on cable.