When this accident happened, there was a pilot that made a statement on these forums, he said that before he did any pre-start checks or anything else, he would say to the other pilot "We agree here and now that when we get an RA, we don't think, we just do it"
Whilst sound advice, and I can see that for you as an ATCO, it seems a priority, history might suggest that if you confine your pre-flight brief to 1 bullet point, the GPWS might be the one to concentrate on! Mountains always have, and I suggest always will, kill more than midairs.
It is quite hard to back away from jumping to conclusions from this report, and proposing "solutions". The real solution was re-emphasised within weeks of the accident. Follow the RA every time... We can see that the "system" failed here, in that the TU-154M Flight Manual was confused over this issue. It is not surprising it was confused, in that the airline only carried TCAS outside the CIS area, and TCAS type procedures were not common to CIS based airlines. That lesson is now learnt.
I do not think it worth getting into discussions / technology for integrating TCAS and ATC. ATC is our prime collision avoidance measure. TCAS only steps in when ATC has (rarely) failed us. Why now involve the "failed system" anymore?
An analogy is a GPWS warning. We primarily avoid mountains by navigation and general awareness. When the GPWS warning goes off, if the pilot now still tries to bring his "situational awareness" into account, he usually fails, and dies. We need to now assume that the GPWS is correct, our navigation has failed, and follow the GPWS faithfully
until the GPWS has shut up
and we can only now try and restore the navigation awareness . Until that point, believe the "last ditch safety system" 100%!
The Mgmt type lessons of course, are overwhelming, and I trust being dealt with...