“'Fitness' is a commonly used word in our society today but within the military it has a particularly deep meaning. Conventionally, being fit means being adapted to a particular condition or circumstance. In war, militaries and their individual combatants must adapt to the chaos and complexities of battle. As these militaries return from war, they must maintain a state of vigilance while also peacefully coexisting within the civil society that produced them. " (Admiral McMullen, USN (Ret))

Social fitness is also interrelated with different aspects of psychological fitness including attention to social cues, regulation of emotion, social problem solving, and adaptability and flexibility to changing cultural and social rules. Likewise, beliefs and appraisals associated with psychological hardiness are thought to enhance one’s ability to both develop and utilize effectively social support systems. (Military Medicine, Volume 175, Aug 2010, pg. 32)

You are not sure in the first place if your team members will buy into this whole concept even if you promoted it over the long haul anyway. Thus you feel as all you would do is just waste your time and theirs on another initiative from the "good idea fairy" that will only last as long as certain personalities are in place.