The NBA is definitely still a big man's league. Without a good big, you don't win. Period. Let's look at the last few NBA champs: LA had Pau, BOS had Garnett, Spurs had Duncan, Heat had Shaq, the Pistons had Wallace, Spurs won a bunch with TD, LA won a bunch with Shaq.
In some cases, the big man in question was not the championship team's leader, as Shaq was the second option on the Heat and Pau is currently LA's second option. However, it is fairly clear that LA and Miami don't win titles, without their bigs. We've seen the decline of the Heat, since Shaq's decline and departure. We have seen the Lakers perform poorly, after Shaq's departure/prior to Pau's arrival.
Conversely, if we switch point guards around, teams have still won, i.e., Fisher and Ron Harper with LA. The Spurs have won with and without Tony Parker.
If we're talking about "Jordan-like" players, of course those can make you competitive. However, they need a great big to win it all, because they are not truly on the level of a Michael Jordan. Those who question this, please refer to the Ewing era, during which the media, along with Sprewell and Houston, claimed that the Knicks were better without Ewing.
Certainly, Spre and H20 were great players. However, upon Ewing's departure, despite having put up good numbers, the Knicks were incapable of winning in the playoffs.