So for the current badges, we have displayed, there are actual applications on the server. People could theoretically directly ask for the help of someone with one of the badges which are shown in-game. if you need help with world edit, you hover over someone's name to see if they have the world edit badge. If you are hoping to have a tour or minigame, you hover over someone's name to see if they have the badge. The sub-team stuff doesn't make sense to be shown. It doesn't help others out, who do not have the badges. It has no direct application to be used or to help others on the server. You can't go like "hm, I wish we had a screenshot taken, let's ask someone to make a screenshot in cinematic.", or "I need a texture to be made... you there with the texture team thing shown, make me a texture at this instance and implement it because I need it now."
Basically, what you're suggesting is unnecessary. It's also unnecessary work to implement.
It has no real application on the server for which it needs to be shown to others.
It would also add a lot of sets of new permissions which can get messy and is not advisable even.
There is no need to have separate ranks or roles or titles for the different leaders of those teams in-game either, depending on the person leading the teams, they have already a manager or a designer specifically appointed to manage or lead those teams. In the case of media, and video team, they are additionally overseen by Toti.
To continue on what green said, there is already a special area in plotworld for people who are developers and who texture to work on, it shows all the available blocks there are for us to use for textures. However, this world is massive since there are a lot of blockstates; It would make texturing a chore to go back and forth between the different states to check your textures. Also why it is preferable for one to texture in their own space to only focus on the blocks they are working with. It keeps it nice, small compact, and focused on only what you're working with. Additionally, the stream server is not necessarily needed for video team things all the time, and people who are not on the video team or media team have to be on the cinematic server from time to time as well. For example, I needed to be on the cinematic server a few times to implement animations for media team purposes. I got quickly whitelisted and could go to work at my own pace. I am not part of the Media team myself, rather I am part of the Animations team, there sometimes is a need for me to be on the cinematics server but not as much, and definitely not enough to justify adding a special role or title with added permissions. It's easier to whitelist people from time to time if they actually have a need to be on the cinematic server, and it's easier to remove whitelist from people too if they need it removed as well.