This thread is not discussing
criminal invasion of privacy, but rather the more mundane "legally selling your info" invasions of privacy. Fortunately, that means we're working with a threat model don't include US citizens fleeing to other jurisdictions.
Illustrative example: Suppose I could get Visa to sign a contract that says they won't sell my personal info. The original parent asked why I would just "take their word" that they won't sell my info.
The answer to that query is that contracts or consumer protection laws with sufficiently punitive clauses are a perfectly fine mechanism.
You counter with Snowden. But... I'm not particularly worried about the CEO of Visa defecting to Russia so that he can tell the highest bidder how often I visit the liquor store. A sufficiently punitive contract with Visa prohibiting the sharing or sale of my information would likely be sufficient deterrent.
Now, figuring out how to get Visa to sign such a contract is difficult, of course. But the actual enforcement mechanism for mandating privacy is straight-forward and doesn't involve crypto foo nonsense.
But even if we were discussing criminal invasions of privacy, I'm not sure how digital tulips are supposed to prevent data exfiltration by an trusted insider. Or, for that matter, preventing the liquor store from selling exactly the same info as Visa by leveraging the facial recognition in their POS system.