The one thing I gather from that graph is that over weekends, IPv6 use spikes. I assume that this means that networks or devices at companies and schools are lagging behind at using IPv6?
Corporate IT tends to lag in these sorts of things. Given that most people have ISP provided CPE, and that's the only device in their homes, it allows the ISP to have a much easier time migrating that user to IPv6. The rollout mechanisms have been well studied.
On the other hand, corporations tend not to have the same level of skill, and focus in terms of networking as an ISP, like a Comcast, or an AT&T. Additionally, they're not as incentivized to move everyone to IPv6, because often times, it's easier, cheaper, and more realistic to buy some IPs.
Moving to IPv6 at the office is a difficult project for most, as there is still a ton of enterprise gear that's IPv6-less. Even at that, enabling enterprise applications with IPv6 tends to be a massive nightmare. Lastly, the security implications of IPv6 are not well understood by most people in the corporate environment.
Yea, there could be a number of reasons for this.
Companies may not see a need to upgrade to IPv6 just yet, all their internal machines have nat-ed addresses and they have enough public ip addresses.
They use some legacy software / hardware X that doesn't support IPv6 (hey, some companies are still paying Microsoft to support XP).
Until quite recently I haven't heard of anyone having a problem with supporting v4 only. But that time is ending; the first problem I've heard of is a VoIP provider who has problems with customers on DS-Lite. In about three years it's quite possible that IPv4 has the sort of occasional tunnel/reliability issues that IPv6 had five years ago.
"Google works, so it's not my connection at fault, it must be your site that's broken."
The big reason to support IPv6 now is IMO that (all else being equal) it's better to add v6 support when you roll something out than to introduce it later.
At work (a larger enterprise in Europe) we already see quite a bit of pain with IPv4. B2B connections are increasingly not using globally unique addressing anymore, so we often need to use prefix NAT and application level proxies to bridge clashing address space. This in turn is a support nightmare and is hurting reliability.
Our network guys seems to love the extra complexity, though.
I hate VPN-ing into other people's networks, it is such a pain-point. As you say, you have address/space clashes, and all kinds of other (sometimes even security) problems.
It sounds easier than it is, the main issue is scaling. Need to connect to one other person for B2B? Trivial. Two? A little harder. Ten, twenty, fifty, ouch...
In the United States, Comcast is one of the largest ISPs that has deployed IPv6, and they've (purportedly) rolled it out to 100% of their residential customers (with supported CPE). However, they're still working on their IPv6 deployment for business customers (still in trial, availability "any day now"). This could account for a lot of it, especially in the US.
