Controversial issues are controversial precisely because there's no "basic sniff test" that fits all the data. If you find you come to an easy conclusion on a controversial issue, you might not have all the information others do. To take your wage gap example, your explanation only works in the case where hiring managers know men and women are equally qualified, but choose to pay women less because they can get away with it. That's almost certainly not what's going on.
You're describing complex issues, not controversial. Controversial issues tend to be controversial because people assume a conclusion, and then defend that to the death - facts be damned. When a sufficient number of people on either side of a topic engage in this behavior, suddenly we have a controversial issue.
So for instance on this case, I agree with you. I've no doubt women get paid less than men on average. And tall men get paid more than short men. And fat men get paid less than non-fat men. And I suspect that if we broke it down into hair color, you'd also find discrepancies there. Differences do not mean discrimination.
A problem would be if companies were unlawfully actively discriminating against people. As you yourself said, that is almost certainly not what's going on.
Disagreeing with you again. Controversy doesn't happen just because people ignore facts. It happens when the facts don't lead to an obvious conclusion, or when there aren't enough facts to go on, so intelligent people can reach different conclusions. When the only people on one side of a debate are obviously stupid or self-serving, we don't call it a controversy. We call it nonsense and make YouTube videos mocking it. (see also, Flat Earth)
> A problem would be if companies were unlawfully actively discriminating
It's a problem that companies discriminate, period, whether they're doing it intentionally or not. Overlooking skilled short people to hire and promote tall people means they're working against their own best interest and against society's interest, at the same time. (That doesn't mean I'm advocating for any particular solution, or that I think height should be a protected class. I'm just saying it is in fact a problem.)
Now you're getting into a touchier issue and making a very large assumption, I suspect without even realizing it. By suggesting that there is a problem you're indicating a belief that you believe all people are roughly identical. As I imagine you may be doing, let's avoid touchier issues and talk about height -- my examples were not off the cuff.
It's extremely difficult to try to objectively measure the competence of an individual in general, but IQ does tend to provide a workable measurement that does tend to be quite predictive and map well to aggregate performance in 'mental' fields. But we're talking about height, so why am I bringing this up? As counter intuitive as it is, height correlates strongly with IQ. We could discuss the possible reasons for this (environmental? sexual selection? shared genetic markers? something else?) but the point is that this is not disputed. Here [1][2] are a couple of sources if you were not aware of this. You can find countless more on google scholar searching for 'height iq correlation'.
But this raises the issue that not only do tall people earn more than short people, but that it's highly likely that companies paying more to tall people are indeed working in their, and society's, best interest. The long and short here is that you cannot assume differences are a result of irrational decisions.
So you're left to try to argue that short people bring something to table that's valuable but less visible than their individual competence (at least in so much as IQ is reflective of that). This could be true, but I think that there's scant evidence for such. The first issue you'd need to overcome is the existential case. And I find the way most people try to do this is by getting back to assuming discrimination, yet now you're stuck in circular logic or having to assume your conclusion. 'All people are equal. What about these vast quantities of data showing substantial differences from ostensibly objective assessments? It's caused by environmental issues and discrimination. Why do you think that? Well because it doesn't show all people being equal!'
And to be clear, everything I'm saying above applies to people considered as groups - not individuals. Einstein, for instance, was about 5'7". It just means there are different distributions among different groups, and so when you consider these groups as a whole you'd expect to see these different distributions reflected.
