American law leans heavily on "reasonableness".

The Fourth Amendment bans only unreasonable searches, and the threshold question is whether someone had an expectation of privacy that society is prepared to recognize as reasonable. That standard is contextual by design (what is reasonable to expect is partly technological, but partly societal and cultural). The "difference in degree" you mention is precisely what is being tested.

The recent (and oft-discussed) Chatrie v. United States is relevant. The Court held that the government's acquisition of a person's phone location history is a search requiring a warrant, and refused to set a duration floor. Their stated rationale was both that even short windows expose sensitive movements, and because they did not believe they could answer how many small violations of privacy add up to a big one. As such, the majority decided that warrants were necessary, lest the government be given a "virtual panopticon"

If we took your hypothetical seriously, an army of officers logging every plate by hand probably isn't a search and there's no reasonable expectation of privacy of movement on a public road. But building a searchable index of those notebooks, and querying it to reconstruct an arbitrary car's six months, is a different act from the observing.

That's the act at issue. Nobody argues a camera needs a warrant to see a plate.

The thing I don't understand: why do so many people want the police to _not_ need warrants to surveil the public? Are you historically illiterate? Are you unaware of how big government power tends to be abused? Do you simply trust that the government will always run by people who will support you and will abuse only the people you personally dislike?

I'm legitimately curious what sort of intellectual position you use to justify your active support of authoritarian measures, and why you don't believe the public should have safeguards against government abuse. My questions might have sounded flippant, but they were sincere. I would like to understand if your position is borne of naïveté, or a sincere preference for fascism.