and more time in the circuit equals more time in a the airspace with the highest traffic density. Think about it - flying three full legs of the circuit probably doubles the amount of time in the circuit compared to an aircraft joining on a base leg. Using that assumption, if adding an extra leg to the circuit does not halve the collision risk per second for the entire flight time in the circuit it has to be counter productive to safety.
I would be very interested to see an objective study on the actual risks of various circuit joining procedures. And I would suggest that if such a study was conducted the risks would be found to be very different in a circuit which has mainly arrivals / departures compared to one which has mainly circuit traffic.