I mentioned the problem
here: the police have no competition. Thus, they have no fear of losing their funding or jobs.
Their funding comes from aggressive appropriation of private property (i.e. taxes). Consumers have no choice in the agencies they hire for security. Regarding a threat to the thugs' jobs, the government's judges are, as Hoppe says, the arbitrators of last resort. Got a problem with the government (police, IRS, DHS, TSA, etc.)? Take it to the judges who are on the government dole.
Good luck with that.
Now, imagine if everything were privately owned, and property rights were defended against every act of appropriation. The "public memorial" wouldn't exist unless a private owner erected it. He could decide who is allowed to visit, and who is not. He could decide what is allowed on his property (much like you do in your home), and what is not. Other private owners could erect their own memorials, and monetize them in any way they choose, or not at all.
As for security, there would be hundreds, and even thousands, of agencies competing for the contracts. Would some personnel, once hired, misbehave? Of course. But their misbehavior would open the door to a number of consequences for the owner (people telling others not to visit, possible judgment against him, etc.).
In other words, the private owners have an incentive to hire the best people for the job. He is unlikely to hire thugs. If he does, few people will visit his memorial.
That's the beauty of pure competition. And it demonstrates the danger of eliminating it from the market. The police have no competitors. It doesn't take a rocket scientist to realize the outcome will be horrible. In fact, there is evidence of it every single day.