I wonder how many mid air collisions we would expect to see if see-and-avoid where entirely ineffectual, or pilots would not look outside ever except to land. I

I wonder how many mid air collisions we would expect to see if see-and-avoid where entirely ineffectual, or pilots would not look outside ever except to land. I have the impression the accident numbers would not be much worse than they are. In other words, my hypothesis is that the fact that there are few mid-airs is owed to ATC, technology (TCAS, TAS) and “big sky”, rather than vigilant pilots.