Yes, but they are allowed to continue to exist under government scrutiny. Most local utilities are set up this way. If you're the first there, you usually get to be the only supplier.
We may just be disagreeing to disagree at this point. I'll let you have the last word here.
This is a one-sided description and a false dichotomy. A non-regulated natural monopoly can be just as suppressive as a government enforced-coercive monopoly. A regulated natural monopoly does not also require the creation of a government-enforced coercive monopoly.
The inefficient private solution stayed the adoption of a publicly administered one.