Among NBA players, there’s very little correlation between a player’s height and how many points they score. Michael Jordan was slightly below average height for an NBA player; Allen Iverson was in the bottom decile. And yet no one would argue the height is irrelevant for someone’s prospects at playing pro basketball: the average NBA player is nearly 6’7″, that is, in the top percentile of the male population.
The relationship between GRE and graduate outcomes is like this. If you take a group that has already been selected on a number of characteristics, including test scores, then there is often only a modest correlation between test scores and outcomes. But exactly the same could be said for any of the other criteria that were used, like GPA, or like the quality of the writing sample or the ever-amorphous assessment of “fit”, if either of the latter were to be assigned scores.
One can not extrapolate from this reasoning to draw conclusions about how people should be selected in the first place. If you did, you’d conclude that nothing departments use to admit students matters much for whether or not they will succeed, and that perhaps the fairest thing to do would just be to admit students completely at random. Admittedly, this would save departments a lot of time.
I freely confess the foregoing are issues I’m touchy about. If it weren’t for standardized tests and grades, I don’t know how I would have been able to attend college in the first place, and honestly I feel the most plausible counterfactual is me managing a convenience store back in Northwest Iowa. If it weren’t for standardized tests and grades, I’m also not sure I would have had the opportunity to pursue a PhD, or at least not at a place as good as the place I did. I do not believe my being in academia is any sort of mistake, that I’m just a lucky impostor. I have been fortunate in many, many sorts of ways, of course. But, especially at the time, how I did on the tasks available to me felt like what was actually within my own control, what I could actually work at and compete on if I wanted to distinguish myself.