The Mavs were head and shoulders the best team in the NBA in 2007, and one of the best organized, most poised teams of all time. They won 67 games IN SPITE OF an 0-4 start to the season. What separated that team from past Mavs teams is that they weren't just the high-octane, fast-paced team of old with an unguardable Dirk but a questionable halfcourt offense and zone defense. The 2007 Mavs had completed the transition to a halfcourt offense, still with an unguardable Dirk but also an elite halfcourt defense. The offense was built on a lot of on-ball screens and forcing switches, to get favorable one-on-one matchups for not only Dirk, but high-post iso specialists like Stackhouse and Howard and to force double teams and net tons of open shots. They didn't shoot a ton of threes and they were near the bottom of the NBA in assists, but they were extremely efficient on a pro rata basis.
The 2007 Mavs were built to beat the Spurs, Pistons and Heat. They were also slightly better than the Suns because they could mix up the tempo dynamically and force Nash into bad situations on defense. Harris, the Mavs PG at the time, was an excellent man defender at his position. The only Suns player who could adequately guard Dirk was Boris Diaw, which forced the Suns into a concession of playing him and Amare together, which reduced their ability to fast break and hit a bunch of 3's.
The 2007 Mavs had one, one, but one fatal weakness: the fast break. Fast tempo, fast break, crazy, smallish (but not-so-small), "death lineup" offenses that featured a bunch of versatile, medium-tall players who were all athletic and proficient at three-point shooting, ballhandling, and on-ball defense. In 2007, there was only one of those teams in the NBA: the Golden State Warriors. They were a poor man's version of their later 2015-2018 "death lineup" le teams, sure, but they were the closest thing to that very concept at the time, and they were full of mojo, gangsta, bad boy mentality, nasty, and underdog spirit. They were 42-40 but better than that record because they didn't make the big trades until the trade deadline. Between Al Harrington, Stephen Jackson and Mickael Pietrus, they had plenty of weapons to mitigate Dirk, and plenty of height to win in the paint on both ends of the court. The Mavericks did not have a tall, low-post threat. In that kind of series, they needed a Duncan or Garnett type to win the chess game, not a Dirk. The "We Believe" Warriors had the horses to match up with everything Dallas wanted to do on both sides of the ball. And, to top things off, Don Nelson knew darn well how Avery Johnson had mastered the Mavericks. An unusual, unlikely perfect storm that provided for possibly the most historic playoff upset in NBA history, one that likely will never be replicated.
However, the Warriors easily were stamped out by a Utah Jazz team that had peaked extremely early in the regular season that year and honestly was not all that great. Boozer, Okur and Millsap were too much for the Warriors in the low post, and the Jazz had one other advantage: Derek Fisher hit threes, at his usual blazing playoff clip. Whereas, Golden State didn't have to respect Devin Harris on the perimeter, so that was a key flaw in the Mavs' game as well. Once again, all about matchups. Matchups carried the day and ultimately were a huge overall benefit to the Spurs, as the two teams that were both built to beat them (the Mavs and Pistons) were eliminated by inferior teams in Golden State and Cleveland, the latter because of a truly epic ECF by LeBron James and Rasheed Wallace's temper ultimately deep-sixing the mighty Pistons.