Father’s Day: Google Doodle provides helpful and cute reminder.
With one of the prototype Big Emotional Episodes named after it, it hints at the importance of where we come from, how much it can define us. Family, friends, educators, everyone and everything that contributes to the ongoing process of making us who we are.
The Doctor has no home to go to, of course, and seemed to have no family (except his granddaughter) long before that. Companions have to be able to run away into time and space, with at best an unreliable promise to have them home in time for tea.
Many player characters in RPGs are orphans (a) because rootless characters can more readily go adventuring and (b) because certain GMs only bring in background details like friends and family to torture players by killing them off.
“Bad news, I’m afraid. Your son is... a player character.”
“What does that mean?”
“It means you’ll both be killed by Orcs before he turns eighteen.”
So choose another way. You could involve a PC’s background regularly whenever they visit their home space-time, those with mysteries in their pasts could have those highlighted, reunions are possible with time travel that could never be otherwise. You don’t have to make the TARDIS totally domestic, and shouldn’t push it on players who aren’t interested, but the ties that bind can still be strong across the gulf of time and space.