Lots of food for thought here--thanks for crafting such a clearly-explained and well-argued piece on a topic that is often neither.

But I think that there is a much simpler way to understand the problems with intersectionality--a different argument that it should be mostly deprecated save as the ELI5 version to motivate why you should use the proper framework instead.

Intersectionality isn't a new idea at all. Statisticians had been using multiple regression for decades prior. Intersectionality is simply an ad-hoc de-mathematized way to express the same idea: outcomes can depend upon more than one variable! Once you notice the parallel, you can then ask questions like: how much of the variance is explained by race? Is there a significant race x gender term? This allows one to deepen one's understanding of what is happening, distinguish important from unimportant effects, correct for other variables, and so on and so forth. Or you can learn that, actually, you don't understand what is going on well enough to be able to distinguish various ideas from each other, and you need to look more carefully before you can be justified in drawing firm conclusions.

But by adopting a vague, descriptive approach, one can substitute all manner of social factors to persuade people instead of actually documenting that one is right. You can just make stuff up, and use various social means to try to get others to believe you. Including exercising power.

In this way, "intersectionality" as a technique is far more vulnerable to abuse than multiple regression. You can try to exploit people's sympathy to effect a power inversion, where the meek inherit the Earth and the formerly powerful are cast down, or you can try to exploit your power to discredit perspectives that are a threat. Regardless, nobody actually knows anything--people have their hunches, of course, and some are right and some are wrong, but we've regressed to a will- and feeling-based approach with all the problems that entails.

And it's not because it's not knowable, either in principle or in practice. In practice, the tools are all there. (And free, even, in R.) It does take skill to use them (quite a lot!) but there's no gatekeeping beyond the reality that some things are complicated and you need to up your game if you're going to grapple with complexity with assurance.

You don't need to critique rationalism. You don't need to take any stance on oppression. You don't need to consider our views on individualism and society. You just need to recognize that it is a strictly inferior approach for understanding things, save for being easy, and use known-to-be-better ways of understanding instead of worse ones.