This is not an accurate understanding of the problem. The entirety of generation capacity for almost all of electrification (except for the last few years and for a very small number of power plants) has been built to handle peak load. Peak load only exists for something like 50 hours out of the entire year. The lights in Time Square represent base load, as they are always on. Turning off the lights in Time Square would do absolutely nothing to manage peak loads as compressors are far and away more energy intensive than lighting is.
The evidence we should be looking for is whether they require turning off AC in commercial buildings during peak load. Instead what we find is that ConEd is literally paying commercial real estate operators to reduce energy consumption during peak while asking residents to do it voluntarily without offering them compensation.
That's how you know the game is rigged. Not through base load lighting, but by literally paying commercial land lords to do something that residents are asked to do for free.