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How do you propose we change human nature?
Why would you want your view changed to appearance and vocal tone should be a major factor in deciding on leaders?
Of course we shouldn't rely on those things, but we do because that's how human brains are wired to varying degrees for different individuals.
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You’re not accounting for the self-fulfilling prophecy effect. It’s not just that tall men with deep voices are unconsciously taken more seriously and regarded as leaders; it’s also that, as these men are growing up, they notice that and begin to regard themselves as leaders in turn. 
So, as a confounding factor for your two statistical arguments, which only can illustrate data trends, not explain them, one could add: short men with higher-pitched voices are less likely to be leaders because they have been less likely to be regarded as leaders by others and so they don’t come to regard themselves as that as frequently as tall, lower-pitched voice men do. 
If you account for the feedback between self-regard and other-regard, you can’t just unambiguously separate “quality” from bias; it turns out that people who fit the natural bias are those who come to possess the qualities in question. >

But as you said, they notice these things, which means that their parents and peers are perpetuating these biases, right? >

Sure, but my underlying point is that you can’t reduce the bias to merely a matter of people’s primitive preferences at work. Rather, the bias is corroborated by its producing the kind of people who conform to it upon noticing its working in their favor. This means that even if you could convince people to recognize the bias as primitive, an evolutionary hand-me-down, it wouldn’t really matter. The choice of tall, deep voiced people would still find corroboration as a good one because those people are the ones who’ve come to regard themselves as leaders and to exhibit the traits of leadership just as a matter of habit.
If it sounds like the argument is circular, it is, but that’s a generic figure of how social facts work. Their arbitrariness (e.g., we could live in a world where short kings lead, idk) has to do with them having their basis in custom, which, in turn, has to do with them having held true in the choice. The basis in custom lends them objectivity as “facts,” where objectivity means that they hold true at the population-level, such as your statistics illustrate. >

I understand that teaching people that these biases are primitive may not work if the bias works in their favor. I may be splitting hairs and possibly speaking irrelevantly or getting too granular; a common saying is that everything must end.
What if a man who has benefitted from these biases has children, but the children are mentally disabled? Or they're not tall and have high-pitched voices; wouldn't they want to subscribe to judging people based on quality, or would they wallow over that which worked for them but won't work for their children?
I think you can break this thinking by telling people that genetics could and possibly will eventually "break," and holding onto the ideas of what strong is will be of great detriment to them.But I may also be underestimating man's ego. >

That wouldn’t work because there would still be other corroborating reasons to believe that tall, deep-voiced men are good leaders: the strongest would be that statistically-speaking, they are, and so you’d be asking people to act against the evidence of their experience.
An alternative strategy wouldn’t be to try and contest a “social fact,” as that rarely work; rather, it’s to offer a different interpretation of existing social practices, so as to make them legible as acts of leadership. 
Social movements have taken that tack in the past, by the way. “Servant leadership,” “horizontal leadership,” “leading with kindness,” etc, are interpretations of behavior that, in the past, wouldn’t have been recognized as styles of leadership. Then, once you have a term, you can corroborate the effectiveness of the style through statistical analysis on the population level. That analysis would make salient features in individuals that would otherwise have been devalued as traits of a future leader: an instance of this would be how we now value (largely in women) a warmer interpersonal style, one that solicits feedback from everyone, as a leadership trait, albeit for a different style of leadership than that expected of deep-voiced, tall men.
So, what the short kings and their advocates need to do is: (1) offer an interpretation of a behavior the kings  already practice that construes it as a leadership trait; (2) demonstrate through quantitative analyses that the trait yields benefits consistently, that is, on a population level; (3) correlate those results to traits that the individuals possess that would explain the behavior. I don’t speak for the kings, though, as I’m 6’ 1” … >

firstly, you yourself invoke value in "stronger".  A CEO is not valuable because of their strength. you seem to have fallen prey to the very idea you critique here.  Perceived or real strength should not matter for a CEO (if it does, then you'd be in trouble because the actual correlations between height and strength are pretty real up until about 6'1, but even then a 6'3" is going to be stronger than a 5'9" person, on average - the correlation in strength increase relative to height increase decreases beyond 6'1ish.)
secondly, the practical requirement of a CEO to be a leader necessitates that they be able to lead in the context of the flawed humans who carry the ideas about height.  I think you misrepresent the challenge here as a "hiring problem" when it's really a chicken and egg problem.  That's not to say it's not a real problem, but in a crazy-world sense do you want to a hire a CEO that your people aren't going to follow?  This isn't a great excuse, and therefore I agree with the "should" in a justice sense, but disagree in the pragmatic sense. >

Could you elaborate on your final point, please? Specifically the first sentence? >

I believe they are saying that there is a vicious cycle at work. Tall people look authoritative -> people obey them more quickly/easily -> identical leading styles yield better results when presented by a tall person ->  more tall people succeed as leaders -> this influences our biases of what a good leader looks like = Tall people look more authoritative -> etc
The very fact we care influences whether or not we should care. We created a flawed, self-perpetuating system with an economic incentive for those in power not to change it.