Courts have held that people have less rights while driving then they do in other settings (such as walking down the street or as a passenger in a vehicle). For example, the doctrine of implied consent allows the government to compel you to submit to a blood alcohol test without a warrant. I wonder if something similar could be applied here.

I certainly support civil liberties, but they need to be balanced against the government's strong interest in preventing the bloodshed that comes from the reckless operation of vehicles.

I think there are many ways you could address this issue that don't involve circumventing constitutional rights.

Most of these systems take a photo of the car, which you can often use to verify who the driver was. For serious offenses you could chose to investigate who was driving and issue a normal ticket rather than an administrative fine. You can create laws about window tinting levels (where they don't already exist), and if you can't identify the driver because the car is violating those laws you can revoke the registration.

You could also institute a point system for vehicle registrations, where if an offense cannot be assigned to a person, it is assigned to the vehicle, and after points exceeded a certain limit the registration is revoked.

I don't know about NYC in particular, but in many jurisdictions a major reason that red-light cameras are treated like administrative fines rather than civil or criminal offenses is to avoid full due-process rights, making it harder to contest the fine, and saving money by making everything automated. Our safety is more important than that.