Yes. Police is regulated and has a lot of conventions (laws) and resources that enforce those conventions. Ultimately, it goes back to a fairly well-resourced court of law, which is willing to take a fairly high cost to make a decision, as a shared cost paid through taxes.

With individuals making those decisions, the decisions will be made at much lower cost, and this will result in lower quality of decisions.

If it’s you using a gun, you get Somalia. If it’s the police using a gun, you get the US. (If it’s the police using a baton, you get the UK). It works because the threat isn’t just physical harm but also social consequences. Even going back through history, there would be governmental consequences for not abiding by fair trade, whether that was the local lord throwing you in the stockades or the rest of your tribe ostracizing you.