No, the reason is that they are empowered to call out bigoted language with terms like "that's racist!" and "that's misogynistic!".

These are strictly stronger defenses of their worth as individuals than is #notallblackinnercityyouth, #notallgodlessheathens, etc., so those happen first.

Members of the supposed dominant group have been intentionally and stridently disempowered from making any such claims by declaring that it's bigotry plus power that the terms apply to, and that the relevant amount of power is mysteriously exactly the amount that the typically-dominant group has over a scale chosen so that they're dominant. So they resort to weaker dignity-protecting protestations.

If you inhabit intellectual spaces where the racist/sexist/etc. terms don't apply, you absolutely see the not all language come out again. For instance, the pushback against "I love women as equals and advocate for women's rights but I hate feminists: they <bad thing>" is almost invariably "not all feminists", "that's not what feminism is about", etc.. (There is, I think, a bit of a difference if someone is solidly in honor culture instead of dignity culture, even in #notallmen, but that goes beyond the scope of this comment.)

It's mostly about natural responses to challenges to self-worth on the basis of what group one has found oneself in.