The issue with intersectionality is the same as the issue with affirmative action: a person is treated as an RPG character where the desired outcome is to "save" the person with the "lowest" stats or compensate for some real or perceived loss in that person's life. In the case of intersectionality, the "winner" is the person who can stack the most "undesirable" traits on his/her bingo card of victimhood (i.e. the victim Olympics) without any consideration given towards his/her personal agency. Intersectionality, both in premise and application, is, in my view, a collection of x-isms of low expectations masquerading as some grand revelation about societal functions.

And I don't think your longterm timeline, even with the nuance and consideration you believe to missing from its application, would bring you to a world where people understand one another's circumstances and integrate these observations into their personal livelihood. Instead what you'll have is a world beset with the reinvention of tribalism and original sin. While intersectionality may have some merit as a sociological observation (even if I though I find its claims to be unfalsifiable), a sociological observation cannot be treated a deterministic inevitability supplanting human agency.