1) Tannery - Tanneries existed under government and freely polluted other peoples land. Sometimes pollution sources have BEEN government associated or driven. There is no "system" that will keep EVERY bad actor from polluting land, water or air which isn't exclusively theirs.
2) Pederasts . See answer above, similar circumstances, different topic. There are many instances where pedos ARE some government functionary, no?
3) Private security. Actual market competition and consumer feedback can keep a private security firm from mimicking governmental coercion based security models. Governmental security models (policing) are already the thing you fear. We already have a domineering extorting control based "security entity", which you can't not pay unless you want to suffer violence from them. They hold a monopoly on the use of force, which is why they can't possibly be an actual security provider, if the first thing they do is prevent competition and force you to pay them, whether you want them or not.
In a free market, consumers would be dumb to pay somebody who doesn't provide the service they want. They'd have actual choice, rather than what exists today, "pay us or else".