> Where I live, people routinely leave bicycles and scooters outside when running errands, routinely take public transport and walk at any time of the day or night without fear and routinely leave delivery packages for collection at the doorstep just to give a few examples because the crime rate is low given strong deterrence

I've lived in places like this, as well. Except it didn't come down to the existence of the police, but the fact that it was a middle to upper middle class neighborhood where nobody had a reason to commit petty theft. Deterrence wasn't a factor at all with the people that lived there when it came to buying and selling drugs like cocaine, for example.

Truthfully, I think most property crime would be stopped in its tracks if people didn't have economic reasons to commit petty theft.

> I think increasingly that people in western societies are misunderstanding (and electing people to positions of power who misunderstand) the big picture purpose that law enforcement and justice system has played throughout civilized history.

If we look at the history of policing in the US, we didn't have municipal police forces for quite some time. In the North in port cities, merchant owners would hire security at their ports, and decided that it would be cheaper to instead make it a government service that everyone pays for instead of just the merchants[1]:

> In cities, increasing urbanization rendered the night-watch system completely useless as communities got too big. The first publicly funded, organized police force with officers on duty full-time was created in Boston in 1838. Boston was a large shipping commercial center, and businesses had been hiring people to protect their property and safeguard the transport of goods from the port of Boston to other places, says Potter. These merchants came up with a way to save money by transferring to the cost of maintaining a police force to citizens by arguing that it was for the “collective good.”

In the South, policing rose out of gangs of slave patrols[1]:

> In the South, however, the economics that drove the creation of police forces were centered not on the protection of shipping interests but on the preservation of the slavery system. Some of the primary policing institutions there were the slave patrols tasked with chasing down runaways and preventing slave revolts, Potter says; the first formal slave patrol had been created in the Carolina colonies in 1704. During the Civil War, the military became the primary form of law enforcement in the South, but during Reconstruction, many local sheriffs functioned in a way analogous to the earlier slave patrols, enforcing segregation and the disenfranchisement of freed slaves.

Ultimately, the origins of policing in the US from wealthy owners wishing to secure their expensive assets from theft, destruction, or in the case of slaves, escape, and also not wanting to pay for that security themselves. Later those police forces served those same owners by serving as strikebreakers[1]:

> For example, businessmen in the late 19th century had both connections to politicians and an image of the kinds of people most likely to go on strike and disrupt their workforce. So it’s no coincidence that by the late 1880s, all major U.S. cities had police forces. Fears of labor-union organizers and of large waves of Catholic, Irish, Italian, German, and Eastern European immigrants, who looked and acted differently from the people who had dominated cities before, drove the call for the preservation of law and order, or at least the version of it promoted by dominant interests. For example, people who drank at taverns rather than at home were seen as “dangerous” people by others, but they might have pointed out other factors such as how living in a smaller home makes drinking in a tavern more appealing. (The irony of this logic, Potter points out, is that the businessmen who maintained this belief were often the ones who profited off of the commercial sale of alcohol in public places.)

[1] https://time.com/4779112/police-history-origins/