To a degree they never had an outright "purchase system' for commissions to begin with. And never anything as pervasive or systemic as Britain for instance.

In large part because the Regular Army especially was so damn small that only a handful of commissioning sources was necessary to fill the slots needed. And the US govt, under the Presidency of Jefferson, acted on this very early. The United States Military Academy at West Point was first founded in 1802, initially meant to provide trained officers for the more technical fields like Artillery, and the Corps of Engineers, but in effect it was the main source of new officers for the entire army, flourishing and setting higher standards of education and professionalism starting with the appointment of Sylvanus Thayer in 1817. Added to this then were the state military institutes, first being Norwich founded in 1819 by the USMA Superintendent before Thayer, but also notably the Virginia Military Institute in 1839, and The Citadel in South Carolina in 1842.

While initially meant to provide a trained body of officers and men for each states' militia, very often the graduates of these schools and other state military institutes could and did seek commissions from the War Department, and serving officers would typically be assigned as instructors, and routine inspections conducted to assess the quality of instruction taking place.

That is not to say patronage did not play a sizeable part in some men receiving commissions, both in the Regular Army(especially when it came to securing appointments to West Point from a Congressman), and Navy where the even smaller officer corps and tiny shore educational establishment meant that recommendations and letters of merit often were what it took to secure a man a Midshipman's slot or sometimes as an Ensign or LT from the Secretary of the Navy. But this really comes to the fore in the States Militia units, particularly those raised for extended service with the national army such as in Mexico or during the Civil War. The Governors of each state had the power to appoint the officers of the regiments by and large, and no small amount of power was expended, or sometimes contributions accepted to secure a young man a certain post. But there was never anything so bald faced as an price listing for a Captaincy or anything like that.

This state of affairs also by and large continues until after the Spanish American War, until the organization of the National Guard with federal control increased. The need for even more trained officers during WW1 and the origins of OCS, and the birth of ROTC out of the examples of Land Grant Acts requiring state universities to teach military tactics starting in 1862.