When we had the lights go out in Toronto, people off the street stepped in to guide traffic until the police officers came along and took over.
(This is clearly why you should all come up and cause a power outage in Toronto so we can all party. Right? Right. :D)
If a set of trafiic lights is broken, such that they are frozen red in one direction and green in another, do not blow through against a red because you “know it’s your turn”! Yes, the light should have turned green at that time. However, there is no way in hell that the crossing traffic will psychically intuit that the green they are seeing is from a frozen traffic light - they are simply going to go through. And they will not be looking out for your entitled ass.
I thought this is what you were supposed to do. I mean, if you’re going straight south, and I’m going straight north, who am I hurting by going through with you? And if you’re going straight south, and I’m facing north, wanting to turn left (west) I’ll pull forward as you do, they way I do at a green light without an arrow, then I’ll turn as soon as my path is clear.
I think your logic is completely correct, and this is usually what I see happen when the lights are out at an intersection. However, as Rufus Xavier pointed out, that’s not what the law (at least in California) says about how you treat a four-way stop.