It's not possible to be an admin without being a user as it's necessary to be an user to access the G Suite admin panel to manage the organization settings.
You could confirm this with the G Suite Sales team.
There are several settings that you could manage to control how your users access Gmail for your organization
From Tailor Gmail settings for your organization
Learn about each setting
End user access settings
To access these settings from the Admin console home page, go to Apps
G Suite > Settings for Gmail > End User Access.
POP and ...
For the moment this is how Google Team Drives is setup. Every Team Drive folder is really a folder for one specific team and about one specific subject. That's why Google restricted moving content between drives for content managers.
Imagine you have Team Drive A with colleagues from team A. And then you have Team Drive B with colleagues from team B. Then ...