The main lesson, as I see the situation: You need a superstar who gets lots of beneficial calls.
"who forces the refs to make difficult decisions about foul calls"
If a star player routinely and very noticeably draws contact, especially close to the basket, it's going to be very difficult for the refs not to make calls in his favor, particularly if the star player is playing in front of a home crowd.
You need a legit MVP candidate, and it helps a great deal if that MVP candidate is elite on both ends of the floor. Of course you have always needed that from the dawn of the NBA. That is why I never put much stock in Boston this year. I expected a better regular season given the depth on the team, but never expected Boston to be a real threat to win the title.
I always thought the idea of this Celts team was to pair elite, versatile team defense and a talented, deep supporting cast with a lead scorer with a deadly jumper and a historically great ability to create shots in crunch time against any amount of defensive pressure.
In other words, keep the game close with great defense and balanced scoring, and then let Kyrie do his thing in crunch time.
Problem is that the defense wasn't good enough, the balanced team scoring wasn't good enough to keep the game close, and the team fundamentally didn't trust each other or the game plan, so as soon as things started to go wrong, they reverted to hero ball and rushed outside jumpers.
I think the plan was sound. The combination of young guys not developing as hoped, Hayward taking longer than anticipated to recover from injury, and the team as a whole not playing together and trusting one another prevented it from coming anywhere close to fruition. Kyrie completely losing his ability to score in the last four games of the team's season sealed the deal.
All of that said, I agree that even in a best case scenario with everything working as expected, the Celts would have been a dark horse contender because they still would have been relying primarily on hitting a lot of timely jumpshots. They were never built to be able to fall back on shots in the paint, free throws, or generating a ton of forced turnovers and fast break points.