My idea is that all projects that are assigned to a team member should be visible to all members on the same team. These projects would be visible on the 'All Projects' tab. This should be a setting that can be turned on or off by team. This would allow more visibility and collaboration within teams...

Tanja, I agree. The current method is overly confusing, especially since in other sections such as 'Reporting', you do click the report and then the option to Copy comes up. I'd suggest that they apply this Copy option uniformly throughout the system.