Good day!
Please tell me why, if the care team can be a member of another team, there is no corresponding role for it?
all roles are suitable only for the person. one role for the Organization (Healthcare related organization). and for care there is none

The CareTeam.participant.role has binding strength of “example”, which means instances are not expected or even encouraged to draw from the specified value set. The value set merely provides examples of the types of concepts intended to be included.

That said, you are welcome to propose a change request to add more example values to the value set.