“I wonder why that is what they believe Old Scratch really looks like?”
You’d need to ask Eliphas Levi, but he’s long dead. Levi is the one who designed the modernized image of Baphomet the statue is based on, though it was based on ancient occultic notions.
The question I want answer is this: Why did Congress commission a statue of George Washingon in the same Baphomet pose?
The statue of Washington is supposed to make you think of a one of the seven wonders of the ancient world, the statue of Olympian Zeus.
European classicism was the deal at the time when Horatio Greenough carved it. People either hated it or made fun of it then, too, but it isn't because of Baphomet. They either saw it as snooty and pretentious, or funny because Washington was bare chested.
From wiki on Horace Greenough's George Washington commission:
Horatio Greenough based Enthroned Washington on Phidias' great statue of Zeus Olympios which was one of the Seven Wonders of the Ancient World (and which was destroyed in late Antiquity).
The statue depicted above is a recreation.
Greenough's work was completed in 1840, Eliphas Lévi's depiction appeared later, in 1850. It's most likely that both used the same iconographic treatment for their subject.