You wrote that sports often teaches students how to be a team member and coordinate with others. True enough, but I think there is a more important educational benefit from sports that does not require team participation or competition nor risk injury.
That is learning to be coachable. Historically coaching was a fundamental part of higher education. In English universities, coaches are called tutors. Elsewhere they were/are known as mentors and guides,
Being coachable or mentorable is one of the most valuable traits of students and adults, whether as a solo practitioner, group leader, or team member.