TCAS is not an air traffic tool, it is a safety/separation tool.
Agree completely that it's not an air traffic tool. It is what is usually referred to as a safety net - that is, something that saves the day when all of the normal systems have failed for some reason. Consequently I find it hard to describe it as a separation tool....because that's what ATC is. I suggest that it is better described as a collision avoidance tool.