teams and putting them in the playoffs?

If rivalries are so important, that would suggest going in the other direction and determining playoff spots based solely (or mostly) on divisional records, which doesn't make sense in the NBA.

The difference between the NFL/MLB and the NBA is that in the NFL (MLB) 67% (75%) of playoff teams are divisional winners, while in the NBA only 37% of playoff teams are divisional winners. So it's impossible to closely tie playoff berths in the NBA to divisional success without reducing the number of playoff teams or increasing the number of divisions ... neither of which is likely to happen.

In the NBA, rivalries are created in the playoffs. So no matter how you determine who gets in the playoffs, it likely won't have a meaningful impact on the number of rivalries that are created.