Ben There -
whats to say, for instance in a busy TMA, that the traffic you think you have spotted and decide to initiate a turn to avoid is
a) the traffic that is generating the RA
or that you will not be
b) causing another RA because you are turning towards traffic that would otherwise not have been a factor?
There is a nice example on record (that happened in UK airspace) of an incident where a pilot thinking he knew better, because of his interpretation of the inherently innacurate azimuth information on TCAS, decided that he was going to be in conflict with an aircraft. The pilot initiated his own turn, without telling ATC, to position his aircraft to cross behind the 'intruder'. He then had an airprox.
The controller had set the 2 aircraft on headings which would have acheived about 12 miles separation, and then went on to concentrate on more pressing matters. He did not see the aircraft make its 'unauthorised' turn and the first he knew about it was when the pilot called an RA descent.
The controller, as is the way, was immediately suspended, subsequently cleared after investigation.
ATCOs are instructed
not to pass turn instructions on receipt of an RA call from a pilot - even though they are far more aware of other traffic that may affect the aircraft in question... unless a pilot sees a clear indication of an imminent collision, he/she should restrict themself to a climb/descent. if it's really that close, then your probably too late anyways, or reacting milliseconds after the the a/c has passed the CPA.
The time you are supposed to visually acquire the intruder is on receipt on a TA, and thats when you should be preparing yourself to initiate a manoeuvre to comply with any subsequent RA... during which you should surely be watching the instruments to in sure you keep in the green zone to give yourself the best chance to ge the most separation, not looking out the window relying on reflexes which, at the closure rates involved, will be lagging behind the facts anyway!
In the unlikely event your manouver creates a new RA-generating conflict,....
not so unlikely - there is another incident, again in UK airspace, whereby multiple - more than just 2 or 3 - RA's were triggered because of the density of traffic around an aircraft that was complying with the original RA... we still have the R/T and radar replays in the training department of our unit (along with other incidents to be used as training aids).