Originally Posted by songbird29
First, there may be an average of 29 seconds before a pilot informs ATC. But that does not mean that ATC is unable to become aware much earlier, when an aircraft deviates from its assigned level.
Even without TCAS RA aircraft are allowed to deviate from their assigned flightlevel. Only if the deviation exeeds 200ft ATC can become aware of the deviation.
As the radarsystems updates the displayed information in intervals, the timespan between begin of the deviation and recognition by ATC can be several seconds.
Even with all these factors for delay, technically there are two institutions trying to control during a conflict situation (ATC and TCAS). These two obviously need to be coordinated in some way.
Originally Posted by songbird29
In the case of an RA, the provision of separation by ATC has failed
This need not be true in all cases. In the case of Ueberlingen, the TCAS RA was issued before the aircraft underrun the 7NM separation limit.