The transition began during the late 80's when defenders began getting more and more athletic. The Lakers and Celtics of the early and middle 1980's were just as physical as the late 80's and early 90's Pistons. The difference was that the Pistons were very athletic - Mahorn, Laimbeer and Salley were all very mobile for big men. Rodman was one of the first players that could guard any player 2-5. The secret to that Pistons defense was their athleticism.
When Jordan was confronted with that athleticism plus the physicality of that time, he was worn down. In the "Bad Boys" documentary, Jordan talks about how he was not ready, either physically or mentally, to compete against Detroit. Pippen talks about much the same thing. And these are two of the most athletic wing players of any era.
So what did Jordan and Pippen do? They hit the weight room to get stronger. Neither guy got all that much bigger - maybe 10 or 15 pounds total - but the difference when giving that added strength to superior athletes was immense.
In an attempt to keep up, more young players started hitting the weights in earnest. Basketball wasn't really a weight lifting sport to that point, but with the athleticism (i.e. explosiveness) increasing, the power game could not be left behind. In the early days, Dr. J was amazing because he did things that literally only a few other players could do. Now, you could probably fill an entire roster with that type of athlete. That means the raw athleticism isn't enough, it must be refined.
You still see lots of tall, skinny guys (Kevin Durant, Kevin Garnett immediately come to mind), but you also see more guys that are powerfully built at every position - a guy like Russell Westbrook would have been something like what David Thompson was when he entered the League if he had come along in the 70's or 80's. How do you compete with that if you aren't an athletic freak? You have to get stronger so you can hold your own against Westbrook, who is actually a pretty lean guy for as powerful as he is.
As for the pick and roll, it came to prominence as more and more guys that could handle the ball began to emerge. Stockton and Malone ran that set for 15 years, but as more PGs with handle and scoring ability began to come into the ranks, it made sense to keep the ball in their hands. Watch any high school game now with a top notch perimeter recruit and you will see that guy handling the ball 80% of the time. Pick and roll makes sure your best perimeter player gets to make a decision on every play. If you have a good perimeter guy and a good inside player (a la Stockton and Malone) even better, because your best two guys will have the ball in their hands on virtually every play.
This was necessitated by the more athletic defenders as well. Average and below average offensive players simply can't compete against the better defenders, meaning they need help getting their shots. Most of the time, that means using your best player (or best two players) to draw the defense away from your lesser players to give them shots they can make. Look at how Golden State used Curry and his shooting to get open shots for everyone else on their roster. By keeping the ball in his hands they were able to exploit the holes in the defense, not only against Cleveland, but throughout the playoffs. Those other guys don't get those shots (and don't have that production) if Curry isn't drawing the defense with the pick and roll.