The existing Internet is a cooperative effort between many companies and countries. That would be cost prohibitive trying to replicate that from scratch because you would need to create the entire infrastructure to get data from point A to point B by wire, fiber optics, satellite, etc. along with necessary network hardware.
It is much more cost effective to connect private networks together using VPNs over the existing Internet. That sends data through an encrypted tunnel. For example that is how we make our office/warehouse LAN in Illinois (and other offices around the country or world) part of our factory's larger private WAN in California 1700 miles away. So we can connect to computers at our factory and our order entry computer there can print directly back to a local network printer in our office.
You would first need to understand what the internet is.
The internet is massive cables which connect countries and even travel across the ocean floor.
So to run a truly private internet you would need to litterly lay your own ocean cables and only people who have access to those cables could access your internet. Which would cost trillions to do and hundreds of millions in upkeep.
The other option is a semi-private internet which uses its own internet protocol. Similar to how tor uses the onion protocol which cannot be accessed by normal browsers.
I'm not asking about intranet in schools, offices etc. A full fledged internet spread globally run by a private firm.
