Team building should not be an assignment by management. It should be an introduction to potential teammates. The team members should take it from there.

I have experienced it so many times where teams are basically randomly generated based on skill sets. Skills are not as important as personalities. Almost all friction on a team I observe is political, not ability related (If I remember right, the number one reason people quit is because of management. Your leader is the most important team mate that you need to vibe with). Building a new skill is much easier than sacrificing a behavior change to kluge yourself into a temporary local system.

I really wish self-managed and self-organizing systems were more widely implemented. We need to eliminate sociopathic oligarchies.