In my experience, Problem #3 was the real productivity killer. On cross functional teams, each person can report to a different manager who has priorities, based on his/her manager’s priorities, and so on. Projects would get stalled all the time, because of differing priorities. Also, what I have seen with having high/medium/low priorities is that the low priorities were really no priority. But, someone high on the org chart had an expectation that the project would get done, because it was listed in a plan. What did work was when a particular project became THE priority across the organization. In that case, the product was highly innovative, was first in its class to market, and quickly established and sustained market leadership.