The number of websites unreachable for not having IPv6 equals 0, so saying your internet is not "up to date" because you don't have IPv6 doesn't mean much
Two things. First, it is nice if you don't have to allocate ports on a NAT box to make a test system available. These days you can't really count on all non-production systems having public IPv4 addresses anymore.
Obviously that only works if all systems that need access have IPv6.
However, the main killer app for IPv6 is your ISP running out of IPv4 addresses. Carrier grade NAT boxes are expensive and introduce all kinds of issues. Better to move as much traffic to IPv6 as possible.
If at some point IPv6 traffic is the vast majority of the traffic for a website, then IPv4 traffic engineering may start to suffer. So technically the site will be reachable over IPv4 for a very long time. But it may be that at some point performance will be a lot worse then over IPv6.
