Fiddling with small percentages
@AC
Obviously you can still connect to the IPv4 internet - after all its going to be around for a while - but it can't keep growing due to the lack of addresses and finer slicing of the smaller free pools is just increasing the size of the global routing tables, which has a knock on effect on the routers that need to process that data. The routers have finite hardware resources to hold and process this data.
Given that you can't cram any more information into 32 bits, then more bits are required to solve the problem, hence the incompatibility between the two versions. This is why its always been called a period of co-existence and why your OS has two IP stacks.
There are some interoperability techniques, that work with different levels of success and different limitations, but don't confuse interoperability and co-existence with actually migrating. The purpose of the dual-stack approach is to allow a painless migration from the older standard to the newer one.
Those who fail to migrate will be the ones left out in the cold once the V4 pools dry up, at which point the pain will really start. New Internet resources won't be able to come up without adopting a V6 only address and without users enabling IPv6, users won't be able to access those sites, so both groups need to do their bit. This is why its called co-existence and parallel running.
As to your point about "IPv4 internet is where everything you want to talk to is", that may have been correct in years gone by, but only because V4 is the incumbent IP version running everything to date, but that's not the same as the "V6 Internet being empty". There are large swathes of IPv6 enabled sites out there.
Look at RIPE's graph of V6 utilisation Here
Also look at Akamai's report of what they see Here
The only thing that is changing is that the time before we hit the wall is decreasing.