I don't see how this argument relies on any property that's specific to privacy (as opposed to other desirable properties). Do you think privacy is special in that way, or that this applies to most similar properties too?
Random examples of properties that could be substituted for privacy and where I'm not sure whether they satisfy the conclusion: "net neutrality for phones" (ability to call anyone, regardless of their phone operator) or non-monopoly-inducing ticket prices on transit (a company can e.g. offer tickets at a price sublinear in distance, so that people will be disincentivized from combining different transit companies in one trip).