I think it would make a lot of sense to rename Teams to Organizations. That certainly seems more the appropriate word for how the functionality has been built where Organization are really largely independent of each other.
I would then suggest actually creating a concept of real teams within the organization also where by one person could be a member of multiple teams but perhaps have a default team.
This change would remove the confusion and lots of change requests asking to see tasks across the top-level constructs. Although some people may for example want to see their Personal and Work tasks together (perhaps also across multiple organizations they work in) it's far less likely.