So, by the contraposition, the transitivity of the implication, and my mathematical powers, having a public IP should be treated as the fundamental right it enables.
Of course, if there are several efficient "implementation details" which enable the layer above, then you just need one of those.
So this notion that we all have a fundamental right to full and fair access to the Internet is already subverted by the fact that we're all default-routed second class citizens of the Internet.
In an overlay network world --- a world that is easier for us to travel to than an all-IPv6 world --- this wouldn't be a problem. Addresses would be inherently portable, multihomed access (both through ISPs and through our friends and neighbors) would be the norm, the notion of "server" addresses and "home" addresses (where you can't take port 25 connections) would be extinct.
Unfortunately --- but very importantly --- this is not equally true of an all-IPv6 world. There is nothing magical that IPv6 does to give us all access to the BGP RIB's of top-tier providers. You're still going to be some ISP's b+tch whether your IP address is 32 bits long or 128 bits wrong.
I'm not arguing that people don't have this fundamental right you want them to[2]. I'm saying that the IP address doesn't actually give it to them. Static IP addresses are just something for geeks to argue about while the telcos continue locking down the Internet.
[1] I'm being presumptive because it simplifies the point I'm making; sorry.
[2] All though I don't think they in fact have that right; things that compromise the "right to IP addresses" are invariably first-world kinds of problems.
Overlay networks sound fantastic. Maybe Eben Moglen's FreedomBox (or something similar) could make it a reality?
[1]: For instance by being a member of a non-profit which itself is the actual ISP.