As it sits today, a user either needs to be a system administrator, the owner of a team, or a member of a team to modify team members.
I can't justify making someone a system admin just so they can manage team membership, and with 200+ teams, can't centralize requests to add/remove someone from a team.
Even a simple Administrative Access option in the access level would suffice - "Allow this user to manage team membership."
Fantastic suggestion! One small issue is that teams are cross-company and cross-group, meaning that group admins technically have no business managing teams. I'd like to suggest a small adjustment to this - if the team owner (creator) is also a member of one of group admin's managed groups, then that group admin should get to manage the team (as if they they were a system admin). Another thing that would be really nice - if system admin, group admin (where applicable), and team owner could decide on which team members are allowed to add other members to the team, currently any member of the team can add others (which isn't the best).