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.
