I'm probably going to start a fire storm here but it could also prove to be an interesting discussion.
In my opinion, just pure see and avoid does not work. If we are not listening to the radio, just looking for traffic, in my opinion we probably see less than 25% of the traffic that comes within 2 miles of us. It's probably closer to 10%.
The reason we think it works is because of something else, the big sky theory. That being that the sky is big and our planes are small. The chances of two planes being in the same place at the same time is remote. Although with the accuracy of GPS and newer autopilots, if we operate along airways this may no longer be the case.
On the other hand; hear, see, and avoid works pretty well. For example, in the traffic pattern if we pay attention to the radio chatter and all the traffic is giving accurate position information, we do a pretty good job of spotting each other. I'd guess something around 75% or maybe even a bit more. Another example would be if we are enroute and talking to ATC either because we are IFR or getting flight following. ATC doesn't always point out all the traffic, and we don't always spot everybody they call out, but we see a lot more than if they didn't call them out at all.
And finally; ADS-B, see, and avoid works pretty well too.
If we know where to look we do pretty well. If we have no idea where to look we don't. Be safe out there.