Well, technically I would say that the fine was for the red-light running, which did happen! (but I see your point!)... but what would stop a road arms race. I would be much happier running an intersection in a huge FWD (SUV, I think you call them), rather than a little hatchback? In which case, it is an issue of vehicle protection vs risk of injury (with no fine), wouldn't that become an issue of might makes right? I think most people would be careful, but there would be enough people who wouldn't to eventually bring the system down.
I would like to believe that people are more altruistic (as a whole, I know that people tend to be altruistic if they can!), but I fear that even two well-intentioned ideas can butt heads hard, leading to a potentially disastrous contest to decide which side backs down. In that case, I would prefer a third party arbiter, preferably one that had mechanisms built in to be accountable and it's power leashed. I would argue that the democratic form (that is by no means perfect!) is currently the best attempt to have that (given that it is under constant scrutiny). Or perhaps, I would better say (given that the leashing doesn't seem to have totally worked always) that other forms are in the long term potentially more disasterous...
In small societies, I do agree that people can structure themselves. I would argue the limit of this would be the size where everyone is able to know the other members.... but on a larger scale, I'm a bit dubious. We see this in public situations (even here on Steemit!), where people are more than happy to screw over someone else to gain a small advantage, essentially socialising risk whilst capitalising benefit. I wish it wasn't the case... and you can't stop people forming bigger societies either, which would have more power than smaller ones.
So, to cut a long story short! I want and wish it were possible to have what you describe, but I'm afraid my faith in the collective individual actions (none of which need to be bad intentioned) is not so strong! On the other hand, I'm happy that there are people like you who also advocate for a different view than mine!