If we didn't use speed cameras, what would be the alternative? Having police officers park at intersections known for speeding, 24/7. Not only is this a waste of money and resources (you would have to divert much-needed officers from more important things like policing high crime areas), it can become dangerous if police officers engaged the motorist, which could lead to a high speed car chase.
Cameras are better because they're just as effective at catching speeders, but without the downsides that come with an actual cop. You don't have to pay them overtime, there's no risk of a chase endangering other motorists or pedestrians, and the police force can focus more on fighting crime.
Speed cameras and other automated devices that catch traffic violators infringe upon citizens' civil rights to move freely throughout America. Law enforcement has a job to do and they have human deputies for that. Until the automated systems get better at detecting who actually drives the car while speeding, such automated cameras are a waste of time. Just because the photo of a car's license plate shows up on camera doesn't mean the car's owner is speeding. Someone else could be driving. The reason police pull over speeders is to see who is behind the wheel and get a driver's license, not just the plates of the vehicle.