Imagine an intersection with 3 independent entrances. Normally 1 is green and 2 red. If everyone runs red lights, then we have cars entering from 3 ways instead of the normal 1. The result is collisions in the middle of the intersection.
"Running a red light" does not just mean "go when it's red" but it explicitly means "transgressing a stop signal". That there can be stop signals on multiple entrances also is complicating and sets up the crash.