I don't mean "rivalries" where the broadcasters are digging way into the vault to find footage of games between entirely different teams. I mean the way you'd expect two very good teams in the same conference to butt heads multiple times, like the Lakers/Spurs/Kings/Mavs in the early aughts, LeBron having to go through the Celtics, the Nash/Stoudemire Suns trying to finally break through the Spurs, etc.
If today's playoff seeding held, in the WC you'd have SAS/MEM as the 1-8 seed, which is both a rematch of last years WCF and a possible repeat of the Grizzlies' upset of the Spurs three years ago, which was also as the 8 seed. You also have Dallas vs. OKC, who have met in two of the last three playoffs.
Without actually checking, I'd say the NBA has more continuity than the other major North American sports leagues, and it produces some multi-year intrigue. While I'm sure lots of people would prefer it the other way, with the more random/diverse matchups you'd get from abolishing conferences, the league would still be giving up a bit of that continuity.