atceng, the thing you are missing is that ATC traffic information is not accurate and precise enough to use for maneuvering. That requires vectoring. Traffic information is a great help since it tells you where to scan for traffic. Following the rules for collision avoidance comes after you have acquired the traffic. If you are drawing geometry in the cockpit you have your priorities all wrong.
But I also think you are concerning yourself with the wrong issue. Midairs do not happen because pilots fail to follow the rules regarding maneuvering to avoid collisions. Midairs happen because pilots fail to see each other. So rather than get distracted by this unimportant tangent, let's focus on the real issue: How to spot other traffic.