True story: at the height of fear about overrunning ICU facilities for Covid-19, a hospital for which a close relative works built a statistical model to predict which patients would benefit most from the ICU. The idea was that if there weren't sufficient beds, they'd triage so the beds went to those most likely to be saved from death, through the ICU interventions. The hospital's diversity committee wanted to modify the model so that a population-matching fraction of various minority groups were always selected (your quota). When told that the model didn't consider race, and that in order to achieve their desired goal, race would have to be added to the model, and artificial weights attached to race in order to bring things into balance (which would be a violation of Federal Law, BTW, as it directly and in a fully documented fashion discriminated in providing care based on race), the response was "That can't be true. If the model worked fairly races would be be treated equally." But it absolutely was true - because some minorities are far more likely to have, and to have untreated comorbidities that worsen outcomes for Covid-19, the model selected fewer of those minorities for the ICU.

So, yeah, for the Diversity Committee definition of fairness, you need quotas.