As a teenager, I never imagined accounting for family in RPGs. Now that I'm a bit on the older side - it just seems natural.
MGT does have the Life Events table which includes quite a number of these elements [
Core pg 34]. Given how much most players enjoy Traveller char gen, I think this table could use some expansion. As others have pointed out - it’s not just filler, but can actively be part of the game - so yeah I think more coverage is appropriate.
Besides expanding upon the Life Events, an additional Random Encounter table (that Zhodani noble ex-girlfriend could be a real pain… :shock

and an NPC table covering relatives (distant cousin the Archduke/serial killer) would be nice.
Imitating RW - this means some player's might have a 'spouse at every port' and motivating factors - like alimony and avoiding certain worlds because of the Ex. (Country Western song theme's as scenarios!).
Firefly is often brought up here - though the show revolved around the ship mates as family - there was still the Tam's parents, Mal’s ‘YoSafBridge’ recurring honeymoon, and don’t forget Jayne's Radar O'rielly style correspondence with his mother (and his cunning hat). These elements, even with this otherwise independent, renegade group, certainly added anchoring flavor to the story and had the series continued would have no doubt factored more into the plots.