I tried an experiment the other day, turning off IPv4 and using only IPv6 on a desktop at home. HN, Ars Technica, Twitter, Facebook... none of them even have an AAAA record. Google does for the main google.com site and for gmail, but not for Google Talk. Hell, even test-ipv6.com doesn't have an AAAA record.
You just jumped to the third phase of the transition plan while the rest of the world is busy doing the first one. That ain't gonna work.
If your IPv6 is working you can't go to the site to test it unless you also have working IPv4.
There is absolutely no reason why test-ipv6.com can't have both an A record and an AAAA record.
Q: Why is this web site reachable via IPv4 only?
You're right, there are no AAAA records, intentionally. A percentage of users are unable to browse sites that are dual-stack. If the users can't connect, then they can't be told they have a problem. This is a big problem facing content providers today; of which, I work at one for my $dayjob. As such, the main test page requires IPv4 (either native or translated).
At some point, when the percentage of "broken" users has gone significantly down, I'll consider making test-ipv6.com dual-stack..
www.v6.facebook.com. 3600 IN AAAA 2620:0:1cfe:face:b00c::3
Maybe on ipv6 day they might put that on the main www.facebook.com name too - no idea.