general relativity - What do we learn from gravity in three spacetime dimensions?

The last decades there has been a lot of research going on in the the area of three dimensional gravity. The motivation, I understand, is threefold:

1. 
   

   Whereas gravity is not perturbatively renormalizable in four spacetime dimensions, in three dimensions it is. To make it even more interesting it has black hole solutions and it is exactly solvable. This opens the way to to study quantum black holes. This make three dimensional gravity a very interesting system on itself.

   
   


2. 
   

   Through the AdS/CFT correspondence there is a connection between conformal field theories (CFT) in two dimensions and gravity in three dimensions. CFT's are important in condensed matter physics and one can use 3D gravity to learn more about them.

   
   


3. 
   

   Gravity in three dimensions is simpler to deal with then gravity in four dimensions. Therefor it can be used as a toy model for gravity in four dimensions.

   
   

I am wondering what are the most important insights that 3d gravity brought in these respects? In particular I am interested in point three: did 3d gravity provide any new view on 4d gravity so far?