I think a big part of the reason the NBA game went to small ball is that the rules , and they way they are enforced, just kept being adjusted to force it to go this way for the purpose of increasing high paced scoring and shooting for entertainment. Stan Van Gundy alluded to this a number of times when he was coaching Dwight Howard in Orlando. The league kept adjusting the rules to allow defenders to get away with more when guarding big men in the post.
Another contributing factor imo is that the league lost many of the top big men prospects, like Greg Oden, Yao Ming, Andrew Bynum, etc. It will be interesting to see if the era of big men returns with the new crop coming up, like Anthony Davis, Andre Drummond, Towns, Okafor, maybe Embiid, or if the league will continue to adjust rules to inhibit low post scoring and promote shooting and fast paced small ball style of play.
Long term, as the rest of the world catches up to the NBA, which they already are, the NBA may have to adjust their style of play to keep pace, as international play highlights fundamentals and teamwork much more, and shooting, which is probably another reason why the NBA pushed their style to small ball already. If you look at recent team USA lineups, they really had no use for guys like Drummond or Dwight Howard. When you have players coming up in international teams like Porzingis who are 7 ft and shoot threes and run the floor while their teams move the ball well, you have to adjust, you can't have guys out there that can't shoot outside the paint, require the ball a lot in the post, and clog up the middle. The US teams had issues with this and with iso basketball in a few past tournaments (see the squad with Lebron, Wade, Dight Howard, and Melo that lost to Greece in the 2006 Worlds a while back, and the 2004 captain Iverson team USA with Lebron, Melo, Wade, and Duncan) before the NBA rules and style were tweaked and the past few squads have adjusted and done extremely well.