> I don't understand why a police cruiser can sit in a public space (or even a private one) and write down licence plates and descriptions of passers-by with pen and paper, or record everything around them with dashcams and bodycams for later use, but when it comes to cameras on a pole this would require a warrant.

There is already plenty of precedent in existing laws that 'automated' is a distinction that matters. Even on this exact issue, a few states prevent you as a private citizen from operating an automated license plate recognition system. You are free to scribble down the plate numbers all you want, but using an automated system is against the law.