[Goose]

And in those situations the organizational leader is responsible in part for allowing that to happen and metastasize to the point of damaging the team.

You are absolutely correct that the coach is responsible for what happens on the team, period. However, "allowing that to happen" may not be in his control. The unfortunate fact is that not everyone on a team can get what they want, both in terms of playing time and strategy. Instilling the willingness to sacrifice your goals for the team is partly the responsibility of the coach. However, no matter what the coach does. some guys are going to be unhappy. How those guys chose to deal with it is a reflection on them. In the abstract, one can say the coach should only recruit guys who have "high character" and who are "team players". Good luck with always making that happen.
I don't have a problem with players leaving because they don't like the scheme or don't feel they can get enough playing time. In some cases, it's true. If you are a rising junior who finds out a freshman is going to get most of your minutes, leaving may make good sense. However, there is a "right way" to do that. The coach can't "make" you give your best effort at that point if you are not willing to give it. This hypothetical situation is not necessarily similar to what actually happened this year with the team, because we don't in fact know the "story" here. This example does however illustrate the limitations of what a coach can actually accomplish in preserving "team cohesion".

[Goose]

And in those situations the organizational leader is responsible in part for allowing that to happen and metastasize to the point of damaging the team.

You are absolutely correct that the coach is responsible for what happens on the team, period. However, "allowing that to happen" may not be in his control. The unfortunate fact is that not everyone on a team can get what they want, both in terms of playing time and strategy. Instilling the willingness to sacrifice your goals for the team is partly the responsibility of the coach. However, no matter what the coach does. some guys are going to be unhappy. How those guys chose to deal with it is a reflection on them. In the abstract, one can say the coach should only recruit guys who have "high character" and who are "team players". Good luck with always making that happen.
I don't have a problem with players leaving because they don't like the scheme or don't feel they can get enough playing time. In some cases, it's true. If you are a rising junior who finds out a freshman is going to get most of your minutes, leaving may make good sense. However, there is a "right way" to do that. The coach can't "make" you give your best effort at that point if you are not willing to give it. This hypothetical situation is not necessarily similar to what actually happened this year with the team, because we don't in fact know the "story" here. This example does however illustrate the limitations of what a coach can actually accomplish in preserving "team cohesion".