IPv6 is (getting more) relevant in parts of the world, because (duh) we're running out of IPv4 addresses. All the backbones and most data centers are already fully IPv6 capable, don't know about cloud providers though. If I rent a bare metal or VPS i can expect full IPv6 connectivity, at least with all the big vendors here in Germany.

We have ISPs here (Unitymedia, one of the largest German cable companies) that have run out of IPv4 and started handing out IPv6-only contrancts to all new customers. Those customers have to access IPv4 resources using DS-Lite /CGN (carrier grade NAT), which is a horrible workaround with a lot of issues. Funny enugh, the same ISPs won't give IPv6 to existing customers because every change will probably lead to increased support costs and make the customer unprofitable.

There was a great talk by a Cisco guy at last year's FOSDEM explaining what to expect with IPv6 and why CGN really, really sucks. Video: https://archive.fosdem.org/2014/schedule/event/no_more_ipv4/

So yes, everyone who serves stuff on the internet should care because you already have or will soon have customers that only have native IPv6 and are best served reliably over IPv6.