George Washington was Lieutenant General (until posthumously promoted in 1976). After Washington, the highest army position (Commanding General/Chief of Staff) was held by Brigadier, Major, and Lieutenant generals until Grant, who was only promoted after the Civil War. The two successors to Grant were also four-star generals but then the Army went back to being headed by Major and Lieutenant Generals until WW1. Even during WW1 era, Chiefs of Staff Tasker Bliss and Peyton March were only temporarily made a full Generals and reverted back to Major Generals at the end of their appointments as Chief of Staff.
It seems European nations had plenty of full Generals and even Field Marshals above them. I understand the US Army was smaller at the time, but during the Civil war, the Army did become very large but was still commanded by Major and Lieutenant generals.
There is little cost to promoting someone to the rank and "General" without any modifiers (i.e. "Brigadier"/"Major"/"Lieutenant") is the obvious rank for person in charge. For example, even small police departments are generally headed by a (full) police Chief, not an Assistant Chief, Deputy Chief or something else lower and I don't know of any small organizations that decided for fairness to larger organizations they should be headed by a "Vice President" because they were too small to warrant a (full) "President". What was the downside of making its Army leaders full generals? Why was the US so stingy to its military leaders including war heroes like Washington in this regard?
The answer to the question of why there were no four star generals prior to 1865 was that the rank didn’t exist and for most of the years prior to 1865 the army was so small and so infrequently used that it made little sense to add additional bureaucracy between the governments civilian leadership and command officers.
During the revolution the most senior officers in the continental army were brigadier generals and major generals. Washington held the rank of Lieutenant General which entitled him to a three star insignia. In 1799, Congress abolished the rank of Lieutenant General and created the new position of General of the Armies of the United States with the intent to bestow that rank on Washington who died before the rank could be conferred on him.
Historically, the US standing army was kept relatively small during peacetime. In fact, after the revolution, the Continental Army was quickly disbanded and the new United States relied on state militias as its sole ground defense. In 1784, the standing army consisted of 80 men in total. For a period of three months, Brevet Major John Doughty was the commander of all US forces such as they were. He is still the lowest ranking person to command the US army.
After Doughty the senior army commander was typically held the title of major general or brigadier general. The only exception being Washington who was named Lieutenant General when he was brought out of retirement in anticipation of the quasi war against the French.
It’s important to remember that from 1789 until the middle of the War of 1812, the total size of the army never exceeded 10,000 soldiers. In fact, congress had a standing authorization of 10,000 soldiers but the number of actual soldiers never exceeded 6,000. Congress clearly didn’t see the need to add additional bureaucracy onto a small fighting outfit that they did not intend to, and in fact rarely, used.
In 1812, Congress contemplating war with Britain, authorized the recruitment of 35,000 soldiers though there were few seasoned officers or NCO’s to lead them. See Center of Military History's publication 74-1, Defending the New Nation, by Dr. John R. Maass. Congress and president Madison overestimated the difficulties in expanding the army from its pre-war size and placed too much hope in state militias to make up the gap.
In fact, the army corp was so depleted of senior leaders that Madison had to pull Henry Dearborn out of retirement. Dearborn, who served under Washington and was the Secretary of War under Jefferson, had resigned that post to be the port collector for the port of Boston. He was ineffective and was removed from that post after only a year.
The United States Army did little more that chase Indians for the next 45 years and though the size of the standing army rose dramatically from roughly 1813 until 1815 peaking at a little over 46,000 soldiers in 1814, it quickly shrank again growing only a handful of times in response to specific campaigns or threats. For example, in 1860 the size of the army is listed as 27,958 while the population of the US was over 31,000,000.