Fair enough. Maybe it's just that I'm used to regular roundabouts so us pulling out in front of someone coming around just felt intimidating I guess. That kind of intersection is why we have traffic-lighted roundabouts. It has the same effect except people are still able to go reasonably fast and not have to break too hard when someone pulls out (since the traffic lights give them plenty of warning).
Well obviously people are really interested about place de l'Étoile in this thread but it's quite amusing as, once you know it for real, it's actually one of our major intesections which works the best in the city. Porte Maillot which is further west crossing the Périphérique, and Place de la Concorde which is further East, are two major intersections generating much more traffic jams than Place de l'Étoile does.
But anyway, the reason why there is no traffic lights within the circle is because the "vehicle on the right way gets priority" rule just works better. Indeed, only the vehicles continuing their road in the circle have to stop. So if you would want to put traffic lights, you would need to separate on the right side the traffic turning right and flowing to the Champs-Elysées, and stop on the left side the traffic continuing within the circle. The problem is that you have 12 avenues joining there, so you have just not enough room to operate this properly. If it was so, the traffic from the avenue Marceau, which is immediately at the left of avenue des Champs-Elysées, would be totally stuck by the vehicles turning right at the Champs-Elysées. Vehicles would need to cross each others at a 90° degree angle, the outcome would be necessarily worse.
But the thing to understand is that it actually works perfectly well. I know that from the outside, watching traffic from the top of the Arc de Triomphe, it looks impressively chaotic but you only need to experience it once by car to realize it couldn't be better organized. As I've just told, Porte Maillot and Place de la Concorde are both much more worrying congestion spots than is Place de l'Étoile.