The most famous of Roman penii statues were found on roadsides throughout the empire as something like guideposts, called a Herm or Hermae (pl.). Often just a square column, with a man’s head and genitalia on it, they were ubiquitous.
And at some later date, someone else took a dislike to all those penii, and systematically smashed them on Hermae throughout the empire.
https://en.wikipedia.org/wiki/Herm_(sculpture)
The ancient Greeks had the herms. In 415 B.C., just before the Athenian expedition to Sicily was set to sail, all the herms in Athens had their phalli broken off. That created a panic—people thought it was part of a plot to overthrow the government. After an investigation they thought they figured out who the guilty men were but scholars still debate what the true story was.
They picked up the practice of using Hermai from the Greeks. Oh, hey, that page you linked has a nice discussion of the Athenian mutilation of the Hermai (hermy-eye), during the slow downward spiral of Athenian (fake) democracy.