The world did not have cops until late in the 19th century.

This is factually incorrect as the first modern police force was created in London in 1829. 1829 is not late in the 19th Century.

https://en.wikipedia.org/wiki/Police?oldformat=true#In_London

Why did it take 10,000 years after cities started?

There are examples of people doing many of the same things as modern police forces. For example, in ancient Athens publicly owned slaves were used for crowd control; Roman vigiles apprehended thieves, runaway slaves and were supported by Urban Cohorts which were heavy anti-riot troops; you had the British constables and Santa Hermandades in Spain during Medieval Europe; Paris created a police force in 1667.

In summation, your claim that there were no cops before the late 19th century is factually wrong on its date for modern police force and factually wrong on the existence of such offices prior the late 19th Century.

https://en.wikipedia.org/wiki/Police?oldformat=true

It wasn't public demand.

Then explain the voluntary policing organizations such as vigilantes and night-watchmen.

Edit: I use a Chrome extension that reformats Wikipedia into a reader friendly format. It is called Wikiwand. However, as not everyone has Wikiwand I wanted to change a source from Wikiwand to Wikipedia.