Yes, because conceptually you're still talking to a computer (it just happens to be a globally load balanced computer). It's still the unicast service model, and it's still fundamentally about building a channel between two operating systems.
Imagine if you dialled a full telephone number, including applicable country code and local regional code, and depending on where you were dialling from, you reached a different telephone in a different geographical location.
As long as it's an answering machine and the message is the same at every telephone reached by this number, it does not matter.
But as soon as you want to reach a live person, and not simply "content", then what?
Is end-to-end about accessing "content" or is it about communicating with someone operating another computer?
I wouldn't want to noodle on this too much. I take your point. Anycast abstracts away some of the notion that you're talking to a specific computer. But the unicast service model is inherently about computers talking to each other. Many, maybe most, of the most important Internet applications aren't about 1-1 conversations, or if they are, they're 1-1 conversations in special cases of systems that also work 1-many.
One opinion is that a very important Internet application will inevitably be 1-1.
Who did the FCC just hire as their new CTO? What is happening to POTS?
1-to-many systems, hacked to give an illusion of 1-1 conversations, e.g. smtp middlemen, social networking's http servers or twitter-like broadcast sms, are what we settle for today, but, imo, this is a limitation not a desired goal.