Any answer to why do you care about hiding this information? can all be boiled down to the fear that "[person or group] might use [private data item] to create [bad outcome] for me."
So the thing people actually care about is the risk of bad outcome, not the actual data itself.
If your theory is correct, then the focus should be on the prevention of asymmetric power imbalances in societal transactions that can even create [bad outcome].