If three extra cars from your direction went through ahead of you when your light was turning red, but you stopped, and on the next half-cycle three cars in the other direction went through when their light was turning red, wouldn't the impediment to your progress caused by the latter group of three cars be offset by the fact that your position in the queue was three cars ahead of where it would otherwise have been?
Obviously there's a limit to how far cars should push a light that's turning red. If there weren't, the light may as well not be there. On the other hand, having the actual hand-off of traffic flow occur a little later relative to the timing of the lights will generally ensure that by the time the hand-off occurs, everybody's intentions are clear. This will, to a certain extent, improve efficiency and safety.
No. I was waiting for a red, and after my light turned green three cars ran the red crossing in front of me and every one entered the intersection after my light turned green. And they were one behind the other. I’ve noticed that a lot in Chicago. My take is that if you get caught BY A COP doing that it should be a serious ticket. But cameras are a) giving tickets for california stops and b) giving tickets at lights where the cycle has been shortened and c) giving tickets if you miss it by a nanosecond. A human cop can use more discretion.