> If the noise in polygenic scores is random, all that will do is reduce correlations. Random measurement error always reduces the ability to observe relationships.

I think you’re misunderstanding how they’re being used (or I am). I think they’re trying to control for genetics via polygenic scores, not trying to establish a relationship between those scores and intelligence. The analogy is that you’re measuring the effect of the price of kids’ socks on their intelligence, and saying the observed effect isn’t due to parental income in some other way, because you’ve controlled for parental income(by controlling for whether there’s a porche in the driveway).