In the documentation page Create and manage an Atlassian team, it mentions:

Unlike organization admins, site admins don’t have these same permissions and must become a members of a team before they can make any changes. Site admins will still need to join a team before they can add or remove members.

It is understood that Teams is something that belongs on an org level, but even then, they are usually managed directly in Jira so it makes sense for site admins to be able to manage teams fully.