The best alternative internet involves an overlay network on top of IP, by encapsulating IPv4 inside IP (basically IPSec).
Only slight modifications need to be made to IPv4.
The fundamental problem is that the Internet address space is controlled by by a single government agency (ICANN).
To prevent one single central authority from controlling the entire Internet, each autonomous system should have the ability to splinter and form its own separate internet. In place of one single Internet, there would exist multiple parallel internets. Each autonomous system becomes truly autonomous, able to leave or join an existing internet.
The advantage of encapsulating IP is that this overlay network benefits from the packet-switching design of IP which overlay networks like Tor lack. For example, IP routing is highly optimized for latency/bandwidth, unlike the convoluted routing methods taken by tor. The low latency makes it suitable for multimedia applications and heavy traffic.
By design, IP packet switching is more suitable for evading censorship of VPNs, because encapsulated packets can easily route around censored nodes.
Encapsulated IPv4 is familiar, predictable, and well documented. Existing software can be reused with virtually no modifications. The extra complexity of IPv6 is likely unnecessary given that the focus is on the free user community, which does not begin to approach 2^32 hosts.
This overlay network will allow users to host from home, since they can be assigned static IP addresses with proper reverse DNS networking. Their location and identity is also obscured by one extra layer of indirection.
In a world of parallel splinternets, the way to communicate with foreign networks is with NAT. Even IPv6 would need NAT
If the world's major powers should go to war, national firewalls would be developed which will cause the Internet to splinter. Without ICANN coordinating IP address space, nations would likely end up with address collisions. Under such a scenario, even IPv6 would need NAT in order to communicate between splinternets.
For example, if two nations claim the ownership of the IP address 2602:fccf:1::, the assumption that each IP address is globally unique will no longer hold true. There would be no way to relay messages between them without resorting to a gateway to translate the addresses, in other words, Network Address Translation.