Thesis Classical phenomenology described one kind of body and called it the structure of experience

This term my reading circle read the fifth chapter of Fanon's Black Skin, White Masks, the one translated as "The Fact of Blackness" in the older English edition and "The Lived Experience of the Black Man" in the newer. My students understood it faster than any philosophy I've given them.

Fanon uses Merleau-Ponty's idea of the body schema, the tacit sense of your body that lets you reach for a cigarette or a match without thinking. Then he describes what happens when a child points at him and says, in effect, "Look, a Negro!" The easy body schema collapses. In its place comes what he calls a historico-racial schema, and below it a racial epidermal schema: he is made to experience his own body through the gaze of others, as an object with a history attached.

My thesis: classical phenomenology, which claimed to describe the universal structures of experience, was describing the experience of a particular kind of body, white, male, healthy, unmarked, and presenting it as the body as such. Fanon's chapter doesn't just add a case; it shows that what Husserl and Merleau-Ponty took as basic was a privilege.

Iris Marion Young's essay "Throwing Like a Girl" makes a parallel argument about women's bodily comportment. Beauvoir's The Second Sex had already made it about woman as "other".

So: was classical phenomenology's universalism wrong, or merely incomplete?