I am not sure if I maybe misunderstood the post, so i just give my opinion on it. I wouldn't like that.
Simply because I want to choose my mods myself, and personally I don't like to mod a channel with someone I can not get along with, just because our streamers are in the same team. Power abuse from mods on twitch is something which often happens, and there are also people who just like the attention and don't work together with other mods, like it is happening in one of the channels I mod.
Then even if in the same team, people are still different. Different values, different approach, different way of working, and not all mods are made to work together, with other mods or streamers. So I would prefer streamers would be able to chose their mods themselves, like that the mod world would become even worse, since mods can't be moderated, which is something that should change in my opinion.
Also not all Mods mod for channels they don't like. So even if in the same team, it doesn't mean that one would like it.

I could see why it might be contentious as it implies a channel giving up the right to mod to a team leader

Alternatively most teams are like minded, so a shared mod option like shared banned list could have a similar result.

How do you become one

Bonsoir l'équipe Twitch.
Je sais que ce n'est pas votre façon de procéder au recrutement des modérateurs globaux pour la Twitch Team.
Pourtant, j'aimerai me consacrer pleinement à cette plate-forme que j'affectionne particulièrement. Il y a beaucoup de choses bien à faire, et je trouve à mon humble avis qu'il manque de modérateur globaux dans les catégories Twitch France.
J'ai pour habitude d'aider les jeunes streamers à prendre en main Twitch, je modère énormément de tchat différents. C'est une évidence pour moi, une réelle passion.
J'aimerai ne serait-ce, qu'avoir la possibilité de participer à vos sélections, ce serait un grand honneur pour moi. Et si je suis sélectionné, sachez que je serai heureux de contribuer à rendre cette plate-forme plus saine et accueillante pour toutes et tous !

i would love to be a global moderator, seeing a lot of things in chat and can't do anything about it except leave the chat isn't always the solution, it would be very helpful seeing a problem and have a solution for it, it will make this platform even more enjoyable.

this would be a really great tool right now!

This actually would be neat.

This is actually a super neat idea! That way, teams can be more than just a promotion tool - there can be a moderation team that operates across the teams channels, without having to individually mod them in every stream. It can also provide a way to easily opt out of that feature, as well as set a level of permissions that’s different from a regular channel moderator.

I honestly already thought this was a feature of teams since I see so many of the same mods in the chats of members of the same team. Why isn't it?

This is a great idea that seems like an overlooked feature of Teams.