Remember DABS?
I thought not. It finally came to me upon awakening this morning. The name before Mode S was Discreet Address Beacon System, pre-1986. Its intent was to allow ATC radar to individually interrogate transponders as needed. However, TCAS came in before more than just a few ATC facilities were equipped.
TCAS needs unique targets for tracking, rather than just blips, so it can make full use of the target aircraft's info, and can increase the discreet interrogation rate in keeping with the level of threat.
A mode C reply or All Call is of more limited use in collision avoidance, in high traffic areas, meaning possible target merging and signal saturation.
GB