Safety and profit don't always coincide.
I think they are a wonderful way for cities to make $$$. The companies that sell, install and manage these things are good at "setting the stage" to ensure that the locations chosen generate the appropriate yield. Yield becomes the primary factor in choosing a location with safety being a secondary concern.
Only good thing, at least in OH is that the tickets are administrative vs criminal. (No driving record issues) It's the way they get around litigation and just get folks to pay.
That being said, in the places where the profit and safety motives actually coincide.. they are good deterrents. More typically, you see them in places just after speed limit changes or where there is significant need to make right turns where right on red is prohibited. Read a presentation from one of the companies showing a "yield curve" based upon the option of choosing the minimum to maximum yellow light period allowed by a state for a given location. It was twice as much $$$ by using the minimum. Guess which one the cities choose.
