The militia’s performance was strikingly bad in the War of 1812. One result was the maintenance of a professional army ever since. I deal with militia as subjects/objects of Republican propaganda in JAMES MADISON AND THE MAKING OF AMERICA, and any account of the War of 1812 — e.g., Hickey’s — will give you the grim story.
Wayne didn’t deal with the organization of the frontier army much differently from St. Clair, but he was a better Indian fighter and was able to defeat the tribes at the Battle of Fallen Timbers. I would say the War of 1812 had much more to do with the creation of a standing army than anything else, though it must be noted that the United States still essentially used a militia system until WWII.