I don't know what to say, except that you're
right. This is the problem that Tor is trying to solve, which is why Tor gets to claim that it is "anonymous," and random websites or apps don't get to make that claim.
I don't think it's a deliberate violation of privacy to operate a website, but I do think that it's a violation to operate a normal website and call it "anonymous." Because, as you point out, it's not.
Not only does it confuse users in the immediate sense, but it poisons the well for everyone who is approaching the problems seriously in the long term.