Without bothering to read the article: High heels were invented to help with stirrups while horseriding. Cowboy boots still have them. If most modern men do not wear them, it might be because they drive cars rather than ride horses.
Actually, they went out of fashion even earlier. The Persians invented them for horseback riding, and then European aristocracy adopted them to look macho; they increased the height until they got impractical, though. Female aristocracy then adopted them during a trend toward male features in women's fashion in the 17th century.
Then in the Enlightenment, men's fashion took a turn for the practical and sober (Man is Rational!) while women's clothing kept the old ostentatiousness (Woman is Emotional and Sentimental!) - including the heels. So by about 1740-60, men's heels had gone definitively out of fashion, while women kept wearing them.
There are a great many things which influence fashion. Available technology. Lifestyle. Cultural trends. Even sometimes practical considerations.
I will suggest though that by the mid 1700s, anyone "important" was more likely to be riding in a carriage than on horseback.
Industrialisation and international commerce led to a new type of self made wealthy business man.
Before then, the super rich inherited their fortune. The established upper class were known for their impracticality to show that they did not have to work - being pale skinned to highlight that they did not labour outside, extravagant clothing to highlight their status, frills etc.
These new self made business men, such as factory owners, were proud of their new status but wanted to distance themselves from inherited wealth. They stuck to practical, but finely made, clothing.
Edit: Having now read the high heel article, they aren't 100% correct about heels being useless in the muddy streets of the era. Staying up out of the mud was part of the point of heeled boots of the three musketeers type era.
Looking through car advertisements, it seems like headrests became common in the mid-to-late Sixties, after hat-wearing had already started to decline.
But have an upvote. It is at least a better argument than the other one so far.