Exactly, PapaBear3625!
Socrates was condemned by a jury of 500 of his fellow citizens (by a margin of some 27 votes) for "corrupting the youth of Athens." So, how did he corrupt them? One gathers he suggested that the Olympians were not good models of morality, or even of reality. The Olympians were just as flawed, just as "disordered" as man. Through this recognition, Socrates "pioneered" monotheism — to the understanding that the order of the Cosmos could not have been established by the Olympians, although supposedly they were responsible for maintaining it. To Socrates/Plato, this clearly pointed to the One God "Beyond" the Cosmos.... That is, to a god who utterly transcends the Cosmos of his making.
Looking back over the whole stretch of human history, this is the second time the concept of monotheism arose. The first was of ancient Egypt and the pharaoh known as Akhnaton, or the Son of the Sun, or Son of the god Aten. He acceded to the throne in 1383 B.C., but didn't rule very long. There is suspicion that he was poisoned. But of course, he had really ticked off the priestly class, what with his insistence on "one" god, rather than the plurality of gods served by the Priests of Thebes.
Anyhoot, this first approximation to "montheism" did not long survive the death of Akhnaton. Egyptian religion and spiritual practice reverted to the "status quo ante" of a pantheon of multiple gods....
Roughly four hundred years before the Incarnation of Christ, it seems Socrates/Plato found the "one God" again. And this time, the concept did not die out.
Indeed, as St. Justin Martyr has told us, the Incarnation of Christ was the "fulfillment" of Greek (classical) philosophy just as much as it was a fulfillment of the Israelite prophecies and history....
Anyhoot, dear PapaBear3625, you are so right (IMHO): The Euthyphro should not be read as a detraction of monotheism or Christianity. It is a "squabble" about the human downside of polytheism.
Thank you ever so much for writing!