Fantastic post.
Mavs actually had the ugliest style in the league after they went from Nash/Nelson to Terry/Avery and went to isoball with Dirk, Josh Howard and Stackhouse.
Early 00s Kings were more like the 2014-18 Warriors offense imo than any other team, Bibby just didn't have quite the shooting % of Curry but similar styles and players overall. Deep team and a ton of motion, cutting, off ball screens and slick passing. Screwed over by the refs and league multiple times. And then the injuries hit and that franchise hasn't seen anything good since. Sad.
Spurs were obviously ran through the inside-out with Timmy alternating with the drive-and-dish with Manu and TP, with consistent elite defense and sometimes hot-and-cold offense which made us a great comeback team but also prone to losing some significant leads.
Suns were a solid defensive team in the Marbury years but then converted to the perennial run-and-gun powerhouse when they swapped him out for Nash. Still a decent defense in terms of DRtg per 100 possessions, but the offense made them special.
Lakers of course were a triangle which meant running the offense through the ball-dominant wing (Kobe) in the high post.
I liked the variation of style, pace and tempo of that era as well. 70% of the battle in those games was about which tempo would carry the day. Obviously when the Suns played the Nelly Mavs or Warriors it was a free-for all and Spurs-Pistons or Pistons-Pacers was always a slugfest, but those inter-style games were great as well. The mid 00s was a great era.
I totally agree with you now that there's just no distinguishing styles anymore as everyone has become a variant of the 14-18 Warriors with the same monotonous gameplan. It's not fun anymore. Coaching these days means very little and the inmates (players) are completely running the asylum now more than ever... both in the game, and even in general management/transactions. As for the game itself today... very little strategy, it's more like a game of War instead of poker.