Thanks @Limi for the feedback!
Mattermost Server 3.6 will have a new team sidebar feature where all your teams will be displayed on the left-hand sidebar.
This will let you use and see all your teams on the same tab - hence without a need to have a separate tab for your teams (in your case, you would just need one open tab)
Stay tuned for the release on January 16th!
Note: The Desktop App won't have an update on the 16th, but the team sidebar will work on the Desktop App v3.4.0 and later