How has IPv4 been able to continue to carry the majority of Internet Traffic (about 69% as measured by Google)? The quick answer is NAT (Network Address Translation), but there is more to it than that. Now we see multiple layers of NAT (e.g. at the home router, ISP, etc).
Fundamental shift of how the Internet works
Because of the limitations of reverse traffic of NAT, there has been a fundamental shift in how we use the internet. Rather than anyone putting up their own webserver and doing peer-to-peer connectivity, servers and services have become centralized in the Cloud, and we access them via a browser (as a client) behind several layers of NAT.
Old becomes New
Computing has, of course, been through this centralized stage before. In the early days, machines were expensive, and terminals were relatively cheap. So a big computer (mainframe, Unix machine, etc) would have many terminals, a client/server centralized architecture. Computers were the scarce resource, so we conserved the few, and hung many terminals off of them.
Fast forward to today
Since it was stated in 1994 that we were going to run out of IPv4 addresses (RFC 1631), the Internet has been slowly shifting to conserve the scarce resource, IPv4 Addresses. And with that the internet shifted to the few services with real IPv4 addresses, and lots of clients behind layers of NAT.
But won’t we run out of IPv4 some day?
Yes, but it is going to take much longer than anyone thought. Because NAT uses the TCP/UDP port numbers as an extension to the address space. By including the TCP/UDP source port (16 bits) + the IP source address (32 bits), it creates a virtual 48 bit address. In a NAT-ed world, we aren’t limited to 32 bits (4 billion) addresses any longer.
With the current Centralized model of the Internet, there is no rush to move off of IPv4.
Cyclical Centralized/Decentralized Fashions
But just like in the 1980s, when the PC was appearing on everyone’s desktop, the Centralized model of computer changed to a decentralized model. It didn’t change because the Big computer manufacturers sold little computers, it changed because people found they could do things with their desktop computers that they couldn’t do (or was too expensive to do) with a Terminal connected to a Big Computer.
IPv6 can also support a decentralized Internet model
IPv4 with TCP/UDP port bits, will give IPv4 a long life, but from now on, it will always be a centralized (in the cloud) model.
IPv6 can also run in the centralized (cloud) model as well. But it can also support true peer-to-peer, or decentralized, networking model as well.
I expect there will be a transition back to a decentralized Internet, because what was old becomes new again, and people will find it better for some application. A current peer-to-peer example app is BitTorrent which is used among other things, to distribute Linux distros. It works best on a peer-to-peer internet.
Once developers realize that a peer-to-peer model might work better for their application, we will see a shift to the technology which supports it, IPv6.