Nicole,
You make many good points! Getting people from different departments to come together for one purpose is an excellent way to design a team. It helps not only to solve an issue but also fosters understanding of the other departments. Cross-training is never a bad thing!
Ideally, the corporation can select individual goals that support the department goals, which in turn support the mission of the institution. Having this alignment means that everybody has a vested interest in doing their best and helping others to succeed as well.
Thanks,
Dr. Jamie Morley