I used to work with an ex-military guy (extremely bright, hard working, excellent leader, etc. etc.).
He was about 64 inches (1.63 meters) tall, balding, and not the handsomest fella. He told me point blank: "I was never going to become a general or achieve any other extremely high rank simply because I didn't have 'the look' or physical stature of a general."
Compare Canada where, beyond not having photos, even gender-based pronouns have been removed from performance reports in order that reviewers not risk gender bias.
If there was one, there was at least a ton of exceptions to the rule, male and female.
EDIT: Though I didn't work with any generals. There are only several hundred U.S. generals, and that number is capped.
That would be gender-blind but also ignores the fact that absolute scale actually matters in war sometimes - running speed, ability to lift and load heavy tank shells for a few hours etc.
One might argue that actual physical strength doesn't matter much. One way to check this claim would be to look at recently granted medals for valor, and see how many of them are related to absolute (not relative) physical prowess.
Indeed, the higher up you go, the more your job becomes about leading and the less it becomes about individual feats of strength. I think you're thinking about the military a little bit wrong here -- this isn't the Roman era (when centurions led from the front and had to be legitimate physical badasses). Being higher up in the military nowadays is a lot more akin to being a paper pusher director at a company.
Medical and fitness are different things. Lots of people can pass the fitness tests but still flunk out for medical reasons. Diabetics. People who get cancer. Failing eyesight. Sever allergies. It is very possible to ace the fitness tests while still failing the medical.
Take Thatcher or Merkel. Both women for whom this arguably matters even more, not attractive, and not even coming from a background that lends itself naturally to climbing hierarchies. Kohl, Merkel's mentor used to often refer to her as his "Mädchen", ('girl', but diminutive, only used for children) and she basically back-stabbed him and took control of the entire party.
There's definitely ways for unattractive or more generally, people who nobody expects to rise to power to do exactly that.
This New Yorker profile from a few years ago is a long read but very much worth it if you want to get a overview. The beginning recapitulates a lot about her childhood so you might want to skip that part if you're only interested in her career.
That's life in general. Even at my company when choosing photos of people to profile to for recruitment posts on LinkedIn, it's pretty clear they lean towards attractive people.
I also notice that with Company Profile page, where who they show is not really indicative of who comprises the company.
There have been several studies on this. Apparently being an attractive woman is a net negative when it comes to being hired by other women (6% fewer callbacks than the same resume with less attractive photo attached in one particular study).
https://www.insider.com/how-chess-was-more-sexist-than-its-p...
Another good example is Xyla Foxlin, who walks a similar line with a YouTube engineering/maker channel and has been very explicit about her approach: "I refuse to “act more like a man” in order to achieve legitimate and respectable success in the professional world. I happen to be someone who embraces her femininity and feels powerful in cute shoes and sparkly makeup, and I don’t see how any of that makes me less of an engineer." [0]
[0]: https://medium.com/1517/beauty-and-the-invisible-beast-c2a8d...
Similarly, a Brigadier General is not the same rank as a General, despite some commonality in word choice between the two ranks.
"These titles are sometimes criticized and some female players elect not to take them, preferring to compete for open titles. For example, Grandmaster Judit Polgár, in keeping with her policy of playing only open competitions, never took a women's title."
You mean like this? https://www.journals.uchicago.edu/doi/abs/10.1086/715141
And in those jobs being good at chess is only part of the equation. You have to be personable, someone that people aspire to. Physical attractiveness is also never a bad thing in the world of streaming. I once chatted with concert violinist. She was not happy about trends in the soloist community. "The moment I saw an exposed midrift in a concert hall, I knew I would never be a soloist."