Dick as I understand TCAS it is not terribly accurate in azimuth. Therefore if one pilot manouvers, based purely on a TCAS TA, they run the very real risk of actually making the situation worse and causing a mid air.
That is why it is drummed into us every 6 mths in recurrent training that you don't turn or manouver based on a TA you merely respond vertically to the RA.
There is an argument that says if you see the aircraft you turn if you think it necesary...my argument would be, in busy airspace, are you sure the aircraft you can see out the window is the same as the TA target aircraft on your TCAS screen?