With net neutrality, piracy and privacy issues... we should indeed expect a "new" internet by 2020.
IPv6 will be the rule of law of course, for one base reason:
IPV4 can not support the growth in emerging markets
and two (interconnected) reasons
- it allows more consumers to connect with more devices
- it allows better tracking - which is a crucial pillar of today's internet sponsorship
Finally, it is the only "partially working" solution today, commercial routers support it, and there is no other protocol that meet today's need and is implemented in most vendors next gen solutions: it has already been tested and accepted by the network's core infrastructure suppliers.
Of course, some custom industrial solutions might need more time to be replaced, but "on the shelf" solutions will be IPV6 before 2020!
SO YES... IPv6 will be mostly integrated (for consumers) before 2020...
In corporations, IPV4 will remain a compatibility issue for a long time, in a similar way that system admins still have to deal with coax cables and VAX or SPARC systems today.