"given no structural impediments" is the keyword - without any structural impediments, all your examples should be true.
Structural impediments aren't inherently unfair - for example, if gay men simply prefer not to be a plumber for some unknown reason, that is enough to say that there is a structural impediment for gay Singoporean plumbers, and there doesn't have to be anything unfair about that.
On the other hand, sometimes structural impediments are immoral and should be rectified. If a whole bunch of gay singoporean men wanted to be plumbers, but weren't allowed to enter the profession as a result of laws against their sexual orientation, that would be an unfair treatment and action should be taken to fix the unfair treatment.
With this in mind, we KNOW that minority populations have been very negatively affected for MANY generations from legal discrimination, which directly caused poverty. It is also widely accepted that family wealth is strongly correlated with success academically, and it is widely accepted that success academically is strongly correlated with socio-economic mobility.
Thus, the basis for affirmative action is that there is a moral burden to rectify structural impediments that are a legacy of legal racism, and that helping oppressed minorities get an education in spite of their circumstances helps propagate the socio-economic mobility that education enables.
You can disagree with many parts of this chain of logic. Perhaps higher education doesn't really help socio-economic mobility. Perhaps the moral burden should not be on universities to rectify past mistreatments. Perhaps you believe there is no moral burden to take action to rectify the legacy of last generations' (and all previous generations') racism & sexism. Maybe you even believe that the absurd underrepresentation of minorities and women in certain fields that were historically limited to white men is not at all tied to said historical oppression but simply due to preference or other factors considered acceptable.
However, examining underrepresentation is not baseless or unscientific, whether or not you agree with the conclusions.