Private policing predates public policing,[0] and so asserting that this is is a new development is not really correct. The same is true, incidentally, of firefighting: private insurance companies formed their own private brigades to protect their policyholders' property.[1] Lots of things that we tend to think of as "naturally" public services have only very recently taken that form.
The first link appears to have died, at least from my point of view, so I’ll just ask — what era was this early private police force from? In Rome for example it seems like a lot of state-like functions were performed by wealthy/prestigious patrons, right? So the line seems a little blurry there.
On the other hand, I wouldn’t be at all surprised to hear that bounty hunters and private security pre-date the police.
[0] See p. 1193 et seq. of this article: https://law.stanford.edu/wp-content/uploads/sites/default/fi...
[1] https://en.wikipedia.org/wiki/History_of_firefighting#Early_...