Private property should be extendable to virtually everything in the world because that would help things run alot more smoothly. It is not as if a person would by Mount Rushmore and then not allow anyone to visit. They would run the place like a business and charge admission by the supply and demand method.
Nearly everything can be classified as private property. If you can buy it or own it, it is pretty much private property. There are very few things that can not be private property. Public lands and things like that will probably never be private property, but almost everything is fair game.
Private property is not extendable to virtually everything in the world. There are laws on owning and declaring private property. If this was the case then everything would already be owned and this is not the case. Public land and waterways will always be public in most cases around the world.
I do not believe private property is extend-able to virtually everything in the world. It is impossible to own public lands, therefore you can't purchase them no matter how much money you have. Hawaii has a similar policy in regards to their beaches, they are all public lands. I'm sure there are other examples.
The misconception of private property is that the land is yours. It is not. The rights to use that land in certain ways belong to you. These rights are afforded to you and protected (or not) by the government. The land that some call private property really belongs to the host nation. The host nation reserves the right to use that land in any way it deems necessary. Thus we have imminent domain laws.