Earlier quoted context omitted.
IQ being public might be problematic; I've heard from more than one lawyer that one ought-not use IQ as a hiring filter, unless you have evidence that the IQ test is not biased against any protected groups. Indeed, hiring from more selective universities is, to a certain degree, a way of laundering hiring based off of IQ, since you can pass the buck to the university itself to not be racially biased.
This is a common predicament. A piece of information that, if it was made public, would be immensely useful in countless ways for the management of our society, But it might also be exploited by bad people. So it is made private. And the icing on the cake. We say "it's private because privacy is intrinsically good and a basic human right ". Not, "It's private because we fear bad people".
Such as?
Now, maybe if one person had an IQ of 80 and the other contender had an IQ of 105 it seems like it could be useful in some particular fields. But for the most part you'll run into the "I'm 200 times smarter than you because my IQ is 102 and yours is 101".
And there is no icing on the cake. Privacy is a multipolar topic and there are many pros and cons around it.
We have rights not because they are some intrinsic part of the universe, or inalienable text written by a deity, we have rights because people working together and learning from the past mistakes in history have decided that something better than what was is attainable, and the moment we forget it something worse will take its place.