How exactly has equality of outcome been "proven to be doomed"? At the aggregate level, at least?
Another issue is we're talking about group level outcomes here - which means we're already accepting that there will be biases in measurements, otherwise the group wouldn't be a 'group' (unless it's literally just skin color which is - a pretty arbitrary/racist way to group people all else being equal).
Those that advocate for equality of outcome desire to make again a slave state, where they as "superior educated white people" can ensure that black people are "taken care of" by ensuring they all have jobs, they all have housing, they all have healthcare, they all have food, and that they have no freedom.