My concern with some "bring your phone and use it immediately" scheme is that someone could pierce the privacy by looking at a correlation between the time an account was mode or a pattern of network-traffic occurred, versus the time someone was using/near the vending machine.

Adding large and unpredictable amounts of latency makes that kind of correlation weaker and hopefully impractical.

That's what I meant by "high latency". Workflow would be something like go to sign up to a site, site issues a challenge which is stored in your browser, then sometime in the next week/month/year you stop by the vending machine which generates a proof for the challenge, then you can finish the signup flow for the site in the next week/month/year.

Of course, this would require people to exercise some restraint with regards to their timing.

But the real problem is that nobody actually wants these types of systems, so there is no demand. The motivation only comes as directives from governments, so it's not about the technically best system but rather whatever corporate parasites manage to lobby for.