"The idea that capitalism solves discrimination magically does not appear to be borne out in any evidence I can find."
We should distinguish between formal legal disabilities ("Jews are prohibited from X by law") from informal discrimination that is the target of modern anti-discrimination law ("Sean Murphy does not want to employ any goddamn Englishmen"). Emancipation has a reasonably good, though not perfect, record. Anti-discrimination is a much newer idea which is much less proven in practice, though for plenty of people, it sounds convincing on paper.
If you look at the European Jews specifically, upon formal emancipation, they were able to establish themselves very quickly, both in business and the academia. In fact much of the subsequent 20th century anti-Semitism was borne out of jealousy of their success.
You won't find many aftereffects of the long-lived Chinese Exclusion Act or Japanese Internment Camps on the current well-being of Asian Americans either.
As for women, they are now outnumbering men in higher education by a considerable margin and, in the young cohorts, outearn them. By the logic of affirmative actions, there should be one for men probably...
It is true that not every group in the world was able to catch up once their shackles were released, but plenty of them actually were, and there was nothing magical about it.
Notably, the one exceptional group that mostly didn't catch up - American blacks - seems to be struggling even with all sorts of formal crutches constructed with the intent to help them. For example, the diversity programs at Harvard et al. seem to be mostly exploited by recent immigrants from Africa instead of generational American blacks.