Unlinkabilty and anonymity is not that hard to demonstrate in the design. At it's core it just means each proof or token is unique each time it is presented, and having no mathematical relation to others (and therefore not tied to any persistent identity either).
Client implementations may need auditing of course to make sure they are doing the right thing. But this is not really different to any other advanced technical system which we rely on every day (e.g. TLS).
As you say though, most of the public don't massively care about privacy (unless you mean their visits to porn sites I guess). But they do seem happy to accept crypto coin security assurances without being crypto experts.
As for "the purpose can change" well - so? That is also true or anything else, it does not seem like a reason to avoid having good protection now. Any change that could compromise that would not be undetectable - the fundamental crypto should not allow it. We would know if it happened.
