I think It might be a little too late to make it a team rivalry thing. The NBA is too star centric now especially with social media and fans being more in touch with their favorite players than ever.. one person is always going to mean more than the team itself..
team rivalries still matter, but player vs player still matters a bit more.
You could do both tho. It’s not like NBA stars wear masks or aren’t already super visible and accessible via social media. It’s just a matter of also putting more of a profile on the team as well.
During the Miami Big 3 we only heard about the superstars. We didn’t get to take into account how a real team culture was developed and made them a player fr. You only get this kinda coverage if it’s the Spurs, Warriors, Lakers, or Celtics. You gotta have insane amounts of team history for the NBA to also use that for promotion.
To me, it makes it lopsided. The player’s legacy is all that matters unless the team has a legacy. Instead of both star and franchise looking for glory/legacy building via championship runs. Only in certain circumstances is that narrative told more evenly.