The resulting desktop instead of email notifications is a function I have somewhat overseen. I agree that this could be useful, specially as long as the different teams are only weakly linked.
My point was only against a general globality in the sense that once a channel is marked as global it would show up for all users irrespective of their team memberships. Even if a channel is marked as global, a user should only be able to join or even see this channel if he is member of the team where this channel is created.
I would even propose that entering that channel would put the user in the team view of the team where the global channel was created so the user gets the right context.