But its not the privacy itself that people care about.

The reason is people care is because this information can be used to harm them.

The reason I care about my credit card number being public is because it can be used to stole my money but If my credit card number can be public while still keeping my money belong to me then I would much prefer that.

The better way would be to make everything as public as much as possible then fixes the issue that arise due to that information being public.