The big sky theory does not apply when planes are converging on the same point in space - like VORs, runways, etc.
I have been flying a long time and I have to tell you that I have near missed a few over the decades.
The one that still pizzes me off was a C150 painted misty grey, in an October drizzle after sundown doing circuits with a student and no lights.
They announced once every go around (they later claimed)
I announced at least twice after leaving approach control.
I came in off an IFR approach (straight in) and supposedly cut him off on the base leg. Never saw him. They came running to my hangar all excited and at first I'm like a deer in the headlights. Then I was pizzed.
Finally I said to the CFI, I'm flying to the FSDO in the morning and filing a complaint against you for operating VFR after sundown with no lights.
Then he looked like the deer in the headlights.