But how are you preventing multiple services from using the same value for service_domain_name because they're cooperating to correlate your use?
Not sending the same value twice would prevent them from being correlated, but now what are you supposed to do when you run out? Running you out could even be the goal: You burn a token to get a cookie and now you can't clear your cookies or you'll be denied a new one since you're out of tokens.
Of course, I think the effective purpose of google's attest feature is to invade everyone's privacy which we should assume is part of why they don't use privacy preserving techniques. Privacy preserving techniques could still be abused, however.
Maybe they're even worse for humanity because they make bad schemes more palatable. I think right now I lean towards no: the public in general will currently tolerate the most invasive forms of these systems, so our issue isn't that they're being successfully resisted and the resistance might be diminished by a scheme which is still bad but less bad.