The problem is that Gould was simply denying reality. It not only can be done, but already has been done, over and over and over again. Unfortunately, Gould turned himself into a classic example of how the deniers on this subject always respond to the facts. I've read many of the articles and such that were printed in response to "The Bell Curve", looking for for any point at which the book's opponents would actually counter the factual claims in the book. It's extremely rare (and so far as I've seen, it has only occurred on one specific issue in one part of the book, not the rest of it). As much as other authors say the book's claims aren't true, they just try to stifle it like all such evidence has been stifled for decades, instead of ever getting around to actually contradicting any of it. Instead they pretend it said things it didn't actually say and "respond" to those instead of its real contents, ignore the ways in which their alternative explanations have already been shown not to work, and rant on and on with emotional appeals standing in for logic and evidence.

Of course, Gould wrote and published "Mismeasure" before TBC was written and published, but he did republish it in response, and this debate didn't begin with TBC anyway; the same methods have been used to deny the existence of unequal human intelligence and its importance to society since long before TBC, and Gould just fit himself right in with the established pattern. They never had facts or logic to support their claims, but they didn't need them; all they needed was the Doctrine Of Fairness, the source of other lies people tell each other to present the world as if it were fair even though it isn't (such as "everybody has some special talent", when we all know some people are good at multiple things and some aren't especially good at anything in particular).

Actually, those are also known to be correlated with intelligence. To dismiss them as uncorrelated is to fail to take into account the difference between statistics and individual-level figures and predictors. No, an individual's brain size does not predict that individual's intelligence. But in a statistical sample including numerous people, the relationship is really there; people with different brain sizes (for their body sizes) have been found to have generally different trends in IQ. A statistical trend has variations built in, but exceptions don't disprove a rule; they just show that there are also other rules at work along with it.

It has been done, but that does not mean that that is the ONLY way studies of intelligence have ever been done. "Sciences" of various kinds have been misused and abused a lot, but that doesn't make real science invalid.