A private street is not necessarily something glamorous. I live in a small townhouse community and our HOA owns a small street.
Why I say it's not glamorous is because we have to come up with ~$100,000 in the next 10-15 years to do major pavement replacement (not resurfacing or sealcoating), because this street is not maintained by the county. For a small townhouse community that has not been properly saving for major capital expenses like this, this is not fun.
I think it was owned by something similar to a HOA. Because the HOA didn't pay a minuscule property tax bill, the private street went up for auction, and a private citizen purchased it. That private citizen now has the ability to charge the residents for use of the street, including the right to park in front of houses.
No. In most places I have lived in the USA, streets are not only public property but they regulate what can be placed within so many feet of the side of the road. So basically, they restrict your land use next to a road, even if you own the property. This is so they can add a sidewalk or expand the road at some point in the future.
Yes, most streets are public and maintained by local government. But anyone who owns sufficient land can build a private street on it. A piece of land doesn't magically become public just because you lay down some asphalt and start driving on it.
If people have to live space on their private land for sidewalks, then when the city does build the sidewalks they are building privately-owned sidewalks.
The difference between public roads/sidewalks and private ones is called "public right of way". Google it. Chances are if you own property along a public street, you own the land to the middle of the street but for all practical purposes, it's controlled by the local government. You have to allow people to travel across your land. This includes sidewalks within the right of way area and they usually are within the right of way.