If you look at probability models there is a weight on importance of each quarter of the game. The 4th quarter has almost a 40% impact on the game (when it should be 25%). I don't remember the exact percentage and it wasn't memorable but having an extra possession in the 4th quarter led to an increase in win probability in close games - threshold is 10 points I think - and a substantial increase in probability in even games.
So the tip off means almost nothing to stat geeks that work for teams for the first quarter possession but the 4th quarter possession is valued so high that it makes it an important thing for a lot of teams. Now there are still a lot of NBA teams that half-ass the tipoff because they aren't looking for the .85% (just making that up) edge but other teams do care.
I know this is more of a comment but just too long but maybe someone can reference the MIT article that I read about this a few years ago. But to sum it up the later in the game you get the more valuable possessions are in their correlation to win probability and you can't get later than the 4th quarter.
In other leagues - not NBA - that us alternating possessions the tip off is even more important because it is a half possession advantage per game. Any coach would want a .55 point lead.