He is highly trained and has far more sensors and options to maneuver than TCAS will ever have and he can to it in very fine tolerances to the last second before collision. He has options until very close proximity and he is specifically trained to operate in a military aircraft unlike TCAS which has 2 dimensional options optimised for civil airliner profiles.
Tourist, I suggest that you read Appendix C to AAIB report into the collision of a Tornado aircraft and Jetranger in June 1993. I think you will be surprised at the amount of time that is needed in order scan, recognise an approaching aircraft, recognise a collision course, decide on action, exicute the control movement and allow the aircraft to resond. According to the report, see and avoid has been described as a maritime concept originally developed for slow moving ships which is now out of place in an era of high speed aviating.
DV