Paul, I don’t have your experience running DitV (just once that I remember), but I’ve played in several games GMed by DitV veterans, so I’ll offer a few thoughts.
First, I think it’s important to differentiate between relationships and Relationships. While the player gets to choose their Relationships, one of the GMs I’ve played under loves peppering towns with people with whom your character has relationships. Your sister who you haven’t seen since she married and moved away, your uncle the millworker, someone you had a crush on when younger and haven’t seen in years–these sorts of things. When they’re a blood relative, per the rules, you automatically get a 1d6 Relationship with them. But more importantly, these relationships serve as invitations to assign Relationship dice and make them a bigger part of the game.
As discussed previously in this thread, there’s certainly the option for the player to see a character and declare, “Oh, that’s my cousin!” to bring in a Relationship. But the GM can also build a town and plan on some of these types of relationships, leaving it in players’ hands whether to pursue them as Relationships.
Second, when I played a Dogs campaign, that GM saw Relationships as a way for players to indicate who they’d like to serve as recurring characters. Obviously, with the way the game is driven by Towns, its episodic structure changes what this means versus more serialized campaigns. But there are plenty of episodic TV shows that nonetheless have secondary characters who appear every now and then.
Ways to handle this in DitV: A Relationship character can get married and move to another Town; their profession can be desperately needed elsewhere and so the King of Life has called them to another Town; a family member passed away, causing a temporary or permanent move to that member’s Town to help look after other family of the loved one; the Dogs can revisit a prior Town. Generally for us, the Dogs get into Town and are surprised to see a familiar face, and then learn why that person is present.
None of this works well if it’s overused, but these sorts of callbacks can feel more natural when used sparingly.
Two other thoughts: I agree that overall, Relationships don’t sing in quite the same way so many other aspects of DitV do. The dice take longer to be assigned (or go unassigned) and are rolled less often than other categories. I don’t know a way to make them feel as essential and intuitive as so many of the other great parts of this game. And second, sometimes Relationships are less useful as dice and more useful as an aspect of character creation. They can be helpful in developing your concept for your character, even if you never end up rolling them or encountering the Relationship character at all. That’s still a useful feature to have in a game.