Why? With privacy extensions (which are normally enabled for user devices), then all someone can do is look at the prefix. This is identical to looking at the IPv4 address in a NAT setup, and it hasn't been that much of a privacy disaster.
As I see it, nothing is lost on that front.
It is not identical unless the OS uses a new IP for every new outbound connection. I believe that would qualify as a (very) nonstandard configuration.
> it hasn't been that much of a privacy disaster.
Indeed, it was tongue in cheek which is why I went on to point out SSO. The reality is most people aren't willing to sacrifice convenience to retain even a shred of privacy.
If you are one of the few who care then you can implement one of the many possible non-standard solutions.