That's a good question!

Fundamentally, sloppy thinking is a threat to humanity's well-being and, in the extreme, possibly even our existence. We have incredibly powerful technology and vast societies for which our intuitions are not ideally adapted. We can navigate these challenges if we are keenly aware, collectively, of the consequences of our behavior, because our intuition for what are good and bad consequences, ultimately, are pretty decent. But sloppy thinking that leads us to predict the wrong consequences leaves us in danger. Thus, in the words of H. G. Wells, "Civilization is in a race between education and catastrophe."

Intersectionality is a good idea as far as it goes, but it doesn't go very far, and people have embraced it to the point of error: coming to wrong conclusions and indulging in antisocial attitudes and behaviors under the guise of correctness and compassion. There are lots of ways make errors of varying degrees--that there is error isn't surprising, but when we detect it we should try to reduce it.

The reason I replied is that you also seemed to have noticed that there were problems with intersectionality as a perspective, at least to the extent that it gets deployed these days. But your reasoning seemed less direct than mine, and less clearly inductive of precise-thinking-where-needed. So I was motivated to share what seems to me a crisper way to point out the problems, which simultaneously offers a cognitive tool that is more precise and thus can better lead one away from error when precision is needed, so that you and your readers could consider it.

I don't think that everything should be quantifiable, measurable, etc.. But I do think it is exceedingly unwise to take demonstrated capability to quantify and measure things, gained with much effort through the labor of many brilliant people, and throw it away in the supposed pursuit of correctness. As a thought experiment, one can consider ways to quantify the beauty of a sunrise, but I wouldn't suggest it. However, if one suggests that hugging criminals reduces crime, one had better actually measure the rates, not just hug some criminals and go, "Yeah I feel like there's less crime now." It might work, but that's not how to know it.

Notions of truth, falsity, and objectivity are incredibly useful for conveying to each other what we can count on and what we cannot. Like most things, when we look closely we can find refinements that can make our thinking even more precise (e.g. confidence intervals, judged-true-but-open-to-evidence-to-the-contrary). But if we attack the foundation with such vigor that we lose even our ability to reliably convey that some things can be counted on and others cannot, then we're strictly worse off: we are more wrong about more things afterwards than we were before, in that more often we will think "Oh, let's do X because that will make Y happen!" and we will do X and Y will not happen.

The reason I've continued to engage is that it seems as though on the one hand you value and have put considerable effort into evaluating the quality of thought that you are engaging in; but on the other hand, seem to have adopted many aspects of a culturally popular but largely quality-decreasing "lens" that has a penchant for tearing down the admittedly imperfect (yet still somewhat functional) and replacing it with nothing or something worse (just more-difficult-to-express-why-it's-worse). That seems like quite a shame, if true, so I thought it was worth diverting from the original topic to attempt to point out where I perceive the problems to be. I could be wrong, of course, either in my suspicion that you advocate for approaches that lend themselves to less correctness, or that by saying anything there is any chance that I would make a difference.

It turns out that I do have some background in statistics and decision theory (and physics), and use them, but it ought not matter for the purposes of this discussion. What use is my claim that I know something if I am not demonstrating it to you, or pointing you to resources that will allow you to know it too?