Don
How your assertion can be quantified, I have no idea. What I can tell you is TCAS has saved my ass a few times. Would it have been a hit, not sure but close enough that TCAS and not a controller separated me from the other player. Not a gig against ATC, separating me from a VFR guy isn't their highest priority in high workload situations. (am I correct with a shade of gray for the type of airspace?) It's my priority however and TCAS likely saved the day.
You can't simply look at TCAS and say that the numbers justify it or not simply based off some empirical data that reflects a singular parameter. The things I use it for day in and day out make it worth its weight in gold. Am I catching the guy ahead on the visual? What's that VFR guy doing over there when landing at an uncontrolled airport or after the tower closes? Is the heavy I'm following a bit high over that fix that I'll cross in a minutes time on profile? Perhaps I should seat the flight attendants as such or adjust my profile.
I'll overlay the TCAS on the WX radar and find gaps in what otherwise looks like a solid line that I didn't see due to radar limitations or display set up. The list goes on and on. Each of those and other uses beyond simply producing RA's make it one of the best tools along with (E)GPWS mandated in the past couple of decades. Remember as you mention Uberlingen that the error of not complying with the TCAS was what allowed the accident to happen. As far as I'm concerned, the pilots have more shoulder more blame than controller as they had the tool in hand to avoid the crash and they are the ones ultimately responsible for the safe operation of the aircraft, not ATC.