A quick look at Gygax's polearm list and any good historical reference to polearms will tell you that Gygaxian design was far less concerned with history than the appearance of history. He makes distinctions that really aren't, and goes well into "overclassification."
Likewise, "Plate Mail" is a completely bogus term. Mail means chain; nothing else is mail. There are a dozen historical kinds of mail, but they all are rings joined together into sheets, and then rigged into a variety of styles of wear.
Gygax's Chainmail rules are not terribly historically accurate, either... they're a good basic set of rules. An introductory game, if you will. Other, far more accurate and simulationist games existed at the same time. Very few, however, were as easy to pick up as Chainmail.
D&D's emphasis on the Gold Piece as the primary currency is again, completely ahistorical. Most people, even the nobles, spent mostly silver coins... usually worth about 1/10th to 1/20th the value of a gold coin, and typically between 200 and 300 to the pound. The monstrously large gold coins of D&D are well beyond the reach of history.
The evidence left us from his rule-systems is one of game over simulation, game over history, and game over realism. Every decision point in the original D&D is, like those in Chainmail, designed for fun and ease of play. A vehicle for story.
Later developments in the game drove it away from the simplicity of both Chainmail and the original rules. But at heart, it's not a historical simulation.
And one of my history professors used to warn people: Anything historical you learned from D&D is almost guaranteed to be wrong.