The Internet is literally a "network of networks", bridging between (locally) autonomous networks operated by different local authorities. That was the big idea in the late 1960s when it was first designed (as the ARPAnet), and the reason it continued to grow from then until now. The ARPAnet didn't use TCP/IP, since it didn't exist at the time. It used an older protocol called NCP (Network Control Protocol) based on a single type of packet router called an IMP. The IMP was a ruggedised Honeywell DDP516, that was connected to local computers at each site. Packets were addressed to each port on each IMP, which meant they were addressed to the computer attached to that port. The day when NCP was to be turned off and TCP/IP turned on across the entire ARPAnet was January 1, 1983. With the dependence on IMPs severed, the IP network router market began to grow with companies like Proteon, 3Com, and most significantly Cisco starting at around the same time. The historic government-funded ARPAnet was rechristened the NSFnet, and many corporate networks joined with IP gateways. The DNS architecture replaced the need to keep HOSTS files at each site updated, and domain name authorities began assigning globally visible names, with the first .COM in 1985.
Like many Unix features, UUCP was a discount version of this communication scheme. It also had support for offline message queueing and forwarding, which made it perfect for organizations without the cash to connect directly to the ARPAnet/Internet. The "bang paths" were required because messages could be sent to sites without a permanent Internet connection, but that were reachable via dial-up UUCP connections. The ARPAnet/Internet itself did not rely on message forwarding through a chain of hosts, since that function was performed by the network routers. (Let's not get into IP Source Routing.)
Today that world seems very far away. I wonder how hard it would be to create an actual "historic arpanet"? You would first need several dozen mainframe computers of all different types, plus terminals and IMPs... Traffic could be channeled through a VPN tunnel.