That won't solve the problem, because there are plenty of good reasons for people to share information with companies that they don't want to share with everyon

That won't solve the problem, because there are plenty of good reasons for people to share information with companies that they don't want to share with everyone. In the case of the Equifax breach, people shared personal information with their lenders; do you think they're going to stop doing that if they're informed? See also my reply to @pishpash below.