Private security is basically how people live in South Africa.
The cops there are either useless, bribed, or too scared to enforce laws so people live in gated communities with a private police force.
I almost want to see the US try this out. Because it will show why cops are needed for society to function. What will happen is wealthy neighborhoods will hire private police forces, business owners will open shops within the confines of those neighborhoods and pay into the private police force to protect their businesses. And the poor/urban areas will see its businesses shut down or moved to the wealthy areas due to heightened crime. The people protesting against police right now are going to be the ones most hurt by their own policy (physically and financially).
The more sensible thing to do would be to unarm regular patrol cops and only bring in the guns for serious situations, like they do in the UK. However, this will never work in the US, because almost anyone can procure a gun, legally or otherwise. If the public is armed, it only makes sense for the cops to be armed.