The quality of the solution(s) is directly related to the competency of the facilitator. Time and again, the quality of the cross-functional team work is affected by commitment and experience of the facilitator.
This has to be the major consideration by companies when they proceed down a path of improvement. In fact, all potential problems will be eliminated or at least minimized by a seasoned leader of the task force.
Cross-functional teams are a great tool. They have produced companies used them many creative and effective solutions. They may be the answer to some of the problems that you are experiencing. If you stay aware from the pitfalls, they can the most powerful management tool that you can implement. Finding and utilizing an effective facilitator in just one part.