Bernd, when setting such a scenario it should be to qualified with the probability of it occurring.
Your example assumes one TCAS inoperative, that the strategic defence has already failed (ATC plan), and that the Controller’s command occurs after the TCAS warning. The latter involving a critical time span of approx 30sec.
Then there is the assumption that the two aircraft will manoeuvre precisely as required to result in a collision.
TCAS will command a minimum descent (1500ft/min ? (check spec values)), the manoeuvre assumes a standard crew response time and acceleration (2sec, 1.25g).
The aircraft responding to an urgent ATC command is not bounded by time or acceleration, but experience suggest that it will not be greater than the TCAS manoeuvre.
Thus there is a vast range of variables in both the start and action conditions that will not result in a collision.
However, given that the initial manoeuvres meet the collision criteria, then TCAS will continue to evaluate the situation and can increase the decent rate attempting to avoid the collision.
If you wish to debate the next level of what-if … ATC demands a higher rate of descent for the non TCAS aircraft, then the whole gambit of time, reaction, acceleration, and TCAS counter-counter response starts again. The practical number of what-ifs depends on the total time span, which provides a limit to the scenario.
No doubt in theory a collision scenario can be generated, but to a simplistic pilot this seems most unlikely and thus we are required to trust the overall controller / ACAS system; ergo training / discipline.
The safety certification should show that the probability of the collision scenario is sufficiently extreme to discount it; thence it meets an acceptable level of safety. The principle of aviation safety is that it is not absolute; it accepts that rare events can occur, but the probability of them resulting in death has to be extremely remote (10-9).
Your approach appears to take the limit case as ‘the’ hazard without qualifying (bounding) it with the probability of its occurrence. Yes it is a real hazard, but if by following TCAS it only occurs in one manoeuvre in 10 million, then the industry accepts that following TCAS is the safer option.