Really, there isn't much said about his career as a battlefield commander because there simply isn't much to say.

Hamilton did certainly agitate for a military command for much of his time on Washington's staff, and when Washington gave him one, it was one of the best feathers in the cap any could have dreamed of throughout the whole war. More on that in a second. Hamilton's most important service, however, was as Washington's political brain and hatchetman during the war.

Washington, by accident or design, started cultivating the "Father of his Country" image early in the war: he never technically campaigned for the commander-in-chief job (despite wearing his uniform to Congress as they considering candidates), and he never directly engaged in the political sniping, rumor-mongering, and backbiting that defined Revolutionary politics. He had Hamilton, and to a lesser extent, John Laurens for that. Hamilton, as the play makes clear, was an excellent writer, and took particular delight in insulting his enemies on paper. While the play focused on Lauren's duel with Charles Lee, far more destructive to the general's career was Hamilton and Lauren's efforts to ruin Lee's reputation after the Battle of Monmouth - an effort so effective that it "Washington had to snatch a draw from the jaws of [Lee's] defeat" has rarely been seriously challenged by historians in the intervening two centuries.

Back to Yorktown. Hamilton was given command of the light infantry battalion in July 1781, just before their march from the Hudson Valley to Yorktown. The light infantry were the best-trained and most physically fit soldiers in the Continental Army, and had seen some of their best use as shock troops - precisely the role they filled at Yorktown when they stormed the outermost British defensive position, Redoubt #10. The plan, a night attack made with the bayonet, was daring, but not his idea. The technique used - pulling flints from the soldier's muskets to prevent accidental misfires and charging solely with the bayonet - required heroic bravery, but had been done by both the British (Paoli) and Americans (Stony Point) during the war. Hamilton worked directly under the Marquise de Lafayette, who really commanded the action. Since the whole action occurred in and around trenches and fortifications, Hamilton never had the chance to show off the mobility and speed of the light infantry; he basically pointed them straight ahead and said "go get 'em."

One episode of Hamilton's command does stand out: when his soldiers first marched into their trench (light troops generally didn't have to do much manual labor in order to keep them fresh and healthy, so their trenches were dug for them), the British greeted them with a volley of cannonfire. In order to show that his men (but really himself) could not be so easily intimidated, Hamilton ordered his men out of the safety of their trench and had them perform parade-ground military drills while the British shot at them. While these delighted the brash young staff officers in both the Continental and American Armies - the men who would help prop up Hamilton's reputation on both sides of the Atlantic, one of Hamilton's subordinates, Captain James Duncan of his battalion wrote, “Colonel Hamilton gave these orders, and although I esteem him as one of the first officers in the American army, must beg in this instance to think he wantonly exposed the lives of his men.”

Hamilton's military service during the federal period was even more political in nature. In the 1790s, Alexander Hamilton led the charge to create a new professional army which could defend the United States against the French. This army, however, was a thoroughly political organization. Recruitment posters, approved by Hamilton, expressly called on Federalists to enlist and seek commission. Once assembled, the army repeatedly harassed, arrested, and beat political dissidents, particularly Republican newspaper editors, under the aegis of defending the government from seditious, Jacobin elements during efforts to put down the Fries Rebellion in Western Pennsylvania. Outrage at the usage of the army helped propel the Republicans to victory in 1800.

So, is there a historical consensus on Hamilton as a military figure? He serves as a useful tool to view military service in the social context of the day: highly political, with bright young officers having a key eye towards their reputation and social advancement. Hamilton was better than most at controlling the narrative of both his enemies' actions and his own, and was not afraid to expose others to violence to maintain that narrative.

Sources:

Crackle, Mr. Jefferson's Army

Lender and Stone, Fatal Sunday (much of this book is an examination of Hamilton's politicking on behalf of Washington after Monmouth)

Martin and Lender, A Respectable Army

Michael Schellhammer, "Alexander Hamilton: Dangerous Man," from the Journal of the American Revolution