There are two scenarios where such a site has been useful to me:
1) Making sure I deprecated the right addresses in the Linux kernel, and that the kernel was using the outgoing address I wanted instead of the one it would pick via RFC 3484, and
2) Making sure IPv6 browsing is working since turning off v4 is a pain in the ass (in the setups I've had to troubleshoot v6 on, not my home network, where it's much easier).
1) Making sure I deprecated the right addresses in the Linux kernel, and that the kernel was using the outgoing address I wanted instead of the one it would pick via RFC 3484, and
2) Making sure IPv6 browsing is working since turning off v4 is a pain in the ass (in the setups I've had to troubleshoot v6 on, not my home network, where it's much easier).