it doesn't suppress targets not considered a threat
It may do.
TCAS has something called 'interference limiting mode' which becomes active when the total ammount of SSR transmissions are such that the frequencies are becoming congested.
Once this happens, TCAS will drop from "full time" tracking more distant contacts and/or those with range opening. Full time tracking is about one update per second, this can be dropped to as rarely as once per 10 seconds.
Only traffic in 'full time' tracking is shown on the traffic display.
Source: Rockwell Collins Advisory Leaflet - Common Causes For TCAS Traffic Dissapearance.
CPB